Topics in elliptic problems: from semilinear equations to shape optimization (Q6592001)

scientific article; zbMATH DE number 7900718

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English	Topics in elliptic problems: from semilinear equations to shape optimization	scientific article; zbMATH DE number 7900718

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instance of

scholarly article

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title

Topics in elliptic problems: from semilinear equations to shape optimization (English)

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author

Hugo Tavares

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published in

Communications in Mathematics

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publication date

23 August 2024

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zbMATH Keywords

elliptic equations and systems

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existence and multiplicity of solutions

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free boundary problems

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least energy solutions

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optimal partition problems

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partial symmetry and symmetry breaking

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Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains

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Classification and stability of positive solutions to the NLS equation on the T -metric graph

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On the Singular Set of Free Interface in an Optimal Partition Problem

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Variational problems with two phases and their free boundaries

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Singularly perturbed elliptic systems

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Standing waves of some coupled nonlinear Schrödinger equations

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Dual variational methods in critical point theory and applications

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Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization

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The second Yamabe invariant

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Minimal partitions and image classification using a gradient-free perimeter approximation

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Nodal solutions of elliptic equations with critical Sobolev exponents

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Problèmes isoperimetriques et espaces de Sobolev

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On the existence and shape of least energy solutions for some elliptic systems.

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Semilinear elliptic equations for beginners. Existence results via the variational approach

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On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain

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The number of nodal domains on quantum graphs as a stability index of graph partitions

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Normalized solutions for nonlinear Schrödinger systems

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Normalized solutions for a system of coupled cubic Schrödinger equations on $\mathbb R^3$

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Normalized solutions of mass supercritical Schrödinger equations with potential

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A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems

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Multiple normalized solutions for a competing system of Schrödinger equations

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Q3409164

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Partial symmetry of least energy nodal solutions to some variational problems

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On an Elliptic Equation with Concave and Convex Nonlinearities

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Normalized solutions for a coupled Schrödinger system

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Existence and stability of standing waves for supercritical NLS with a partial confinement

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On entire solutions of an elliptic system modeling phase separations

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Critical partitions and nodal deficiency of billiard eigenfunctions

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A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results

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A Paneitz-Branson type equation with Neumann boundary conditions

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Hamiltonian elliptic systems: a guide to variational frameworks

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Paths to uniqueness of critical points and applications to partial differential equations

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Nodal Solutions for Sublinear-Type Problems with Dirichlet Boundary Conditions

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Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems

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Radial positive solutions of elliptic systems with Neumann boundary conditions

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Numerical simulations for nodal domains and spectral minimal partitions

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Optimal Partitions for Eigenvalues

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Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

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Lipschitz continuity of state functions in some optimal shaping

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Variational methods in shape optimization problems

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Q4225519

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Multiphase Shape Optimization Problems

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Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditions

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Q4459637

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An optimal partition problem for eigenvalues

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Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries

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On a long range segregation model

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Bose fluids and positive solutions to weakly coupled systems with critical growth in dimension two

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The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain

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A sign-changing solution for a superlinear Dirichlet problem

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Orbital stability of standing waves for some nonlinear Schrödinger equations

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Q4434430

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Some existence results for superlinear elliptic boundary value problems involving critical exponents

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A one-to-one correspondence between the static Einstein-Maxwell and stationary Einstein-vacuum space-times

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Note on ground states of a nonlinear Schrödinger system

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Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates

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Asymptotic Behavior of Least Energy Solutions for a Critical Elliptic System

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Sign-changing Solutions and Phase Separation for an Elliptic System with Critical Exponent

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Positive least energy solutions and phase separation for coupled Schrödinger equations with critical exponent: higher dimensional case

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An optimal constant for the existence of least energy solutions of a coupled Schrödinger system

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Bifurcation and segregation in quadratic two-populations mean field games systems

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Critical polyharmonic systems and optimal partitions

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Multipeak solutions to the Bahri-Coron problem in domains with a shrinking hole

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Existence and phase separation of entire solutions to a pure critical competitive elliptic system

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Yamabe systems and optimal partitions on manifolds with symmetries

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Fully nontrivial solutions to elliptic systems with mixed couplings

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Phase Separation, Optimal Partitions, and Nodal Solutions to the Yamabe Equation on the Sphere

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A simple variational approach to weakly coupled competitive elliptic systems

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Minimal nodal solutions of the pure critical exponent problem on a symmetric domain

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Multiple solutions for the Brezis-Nirenberg problem

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Positive splutions of semilinear elliptic systems

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On a semilinear elliptic system

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Existence of solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary condition in general domains

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Nehari's problem and competing species systems.

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An optimal partition problem related to nonlinear eigenvalues.

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On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae

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Characterization of ground-states for a system of $M$ coupled semilinear Schrödinger equations and applications

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Ground-states for systems of $M$ coupled semilinear Schrödinger equations with attraction-repulsion effects: characterization and perturbation results

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Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with $d\geq 3$ equations

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The effect of domain shape on the number of positive solutions of certain nonlinear equations

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Q3645667

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Regularity of the free boundary for the two-phase Bernoulli problem

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Optimal uniform bounds for competing variational elliptic systems with variable coefficients

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Solutions to a cubic Schrödinger system with mixed attractive and repulsive forces in a critical regime

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The effect of linear perturbations on the Yamabe problem

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Q5189317

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Self-focusing on bounded domains

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Stationary problem related to the nonlinear Schrödinger equation on the unit ball

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An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients

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New monotonicity formulas and the optimal regularity in the Signorini problem with variable coefficients

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Existence and orbital stability of standing waves for nonlinear Schrödinger systems

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Multiple positive normalized solutions for nonlinear Schrödinger systems

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Stability theory of solitary waves in the presence of symmetry. I

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Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two

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Sharp concentration estimates near criticality for radial sign‐changing solutions of Dirichlet and Neumann problems

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Asymptotic behaviour of a semilinear elliptic system with a large exponent

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Solutions of an elliptic system with a nearly critical exponent

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The existence, uniqueness and nonexistence of the ground state to the<i>N</i>-coupled Schrödinger systems in $ \newcommand{\R}{{\mathbb R}} \boldsymbol{\R^n (n\leqslant 4)}$

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Q3084648

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Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent

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Critical sets of solutions to elliptic equations.

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Quantitative properties of ground-states to an $M$-coupled system with critical exponent in $\mathbb{R}^N$

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The Brézis-Nirenberg type problem for the $p$-Laplacian: infinitely many sign-changing solutions

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An existence result for sign-changing solutions of the Brézis-Nirenberg problem

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On spectral minimal partitions: a survey

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Nodal domains and spectral minimal partitions

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Nodal minimal partitions in dimension 3

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On Spectral Minimal Partitions: the Case of the Sphere

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Shape optimization and spectral theory

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Existence of solutions with prescribed norm for semilinear elliptic equations

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Orbital stability of ground states for a Sobolev critical Schrödinger equation

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Multiple normalized solutions for a Sobolev critical Schrödinger equation

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Rearrangements and convexity of level sets in PDE

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Q5732050

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Regularity for Shape Optimizers: The Nondegenerate Case

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Quantitative uniqueness for second-order elliptic operators

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Uniqueness of positive solutions of $\Delta u-u+u^ p=0$ in $R^ n$

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3 Regularity of optimal spectral domains

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The Yamabe problem

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Large amplitude stationary solutions to a chemotaxis system

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Nodal sets of solutions of elliptic and parabolic equations

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Erratum: Ground state of $N$ coupled nonlinear Schrödinger equations in $\mathbb R^n$, $n \leq 3$

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Ground state of $N$ coupled nonlinear Schrödinger equations in $\mathbb R^n$, $n \leq 3$

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Spikes in two coupled nonlinear Schrödinger equations

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Ground States and Bound States of a Nonlinear Schrödinger System

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Positive solutions for a weakly coupled nonlinear Schrödinger system

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Minimal energy solutions for cooperative nonlinear Schrödinger systems

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Regularity of the optimal sets for some spectral functionals

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Regularity of the optimal sets for the second Dirichlet eigenvalue

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Infinitely many solutions for elliptic equations with non-symmetric nonlinearities

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Normalized solutions to mass supercritical Schrödinger equations with negative potential

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Principal spectral curves for Lane-Emden fully nonlinear type systems and applications

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Multispike solutions for a nonlinear elliptic problem involving critical Sobolev exponent

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Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains

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Sign changing solutions to a Bahri-Coron's problem in pierced domains

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Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition

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Convergence of minimax structures and continuation of critical points for singularly perturbed systems

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Existence and orbital stability of the ground states with prescribed mass for the $L^2$-critical and supercritical NLS on bounded domains

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Stable solitary waves with prescribed $L^2$-mass for the cubic Schrödinger system with trapping potentials

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Normalized solutions for nonlinear Schrödinger systems on bounded domains

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Ground states for a nonlinear Schrödinger system with sublinear coupling terms

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Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems

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Existence and non-existence of positive solutions of nonlinear elliptic systems and the biharmonic equation

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Normalized concentrating solutions to nonlinear elliptic problems

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On elliptic systems with Sobolev critical growth

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On coupled nonlinear Schrödinger systems with mixed couplings

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Normalized bound states for the nonlinear Schrödinger equation in bounded domains

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The Ljapunov–Schmidt Reduction for Some Critical Problems

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Locating the peaks of the least energy solutions to an elliptic system with Neumann boundary conditions

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Existence of Solutions to a Slightly Supercritical Pure Neumann Problem

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Existence of Solutions on the Critical Hyperbola for a Pure Lane–Emden System with Neumann Boundary Conditions

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On Coron's problem for weakly coupled elliptic systems

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A fountain of positive bubbles on a Coron's problem for a competitive weakly coupled gradient system

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Spiked solutions for Schrödinger systems with Sobolev critical exponent: the cases of competitive and weakly cooperative interactions

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A Bahri-Lions theorem revisited

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Extremality conditions and regularity of solutions to optimal partition problems involving Laplacian eigenvalues

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Spike-layered solutions for an elliptic system with Neumann boundary conditions

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Proof of two conjectures of H. Brezis and L. A. Peletier

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The Gross–Pitaevskii equation and Bose–Einstein condensates

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On the bound states of the nonlinear Schrödinger equation with a linear potential

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LEAST ENERGY NODAL SOLUTIONS OF THE BREZIS–NIRENBERG PROBLEM IN DIMENSION N = 5

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Q3645669

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Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions

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On the least-energy solutions of the pure Neumann Lane-Emden equation

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Partial Differential Equations in Action

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Least Energy Solutions for Nonlinear Schrödinger Systems with Mixed Attractive and Repulsive Couplings

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On the Brézis-Nirenberg problem

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Conformal deformation of a Riemannian metric to constant scalar curvature

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On the existence of solutions of Hamiltonian elliptic systems in $\mathbb{R}^N$.

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Least energy solitary waves for a system of nonlinear Schrödinger equations in ${\mathbb{R}^n}$

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On existence and phase separation of solitary waves for nonlinear Schrödinger systems modelling simultaneous cooperation and competition

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Normalized ground states for the NLS equation with combined nonlinearities

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Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case

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New existence and symmetry results for least energy positive solutions of Schrödinger systems with mixed competition and cooperation terms

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Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping

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Variational problems with long-range interaction

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Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius

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The nodal set of solutions to some elliptic problems: singular nonlinearities

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The Unique Continuation Property of Sublinear Equations

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Uniform bounds for strongly competing systems: the optimal Lipschitz case

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On optimal shape design

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Regularity of the nodal set of segregated critical configurations under a weak reflection law

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Sign-changing solutions of competition-diffusion elliptic systems and optimal partition problems

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Existence and symmetry results for competing variational systems

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Existence of least energy positive solutions to Schrödinger systems with mixed competition and cooperation terms: the critical case

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Least energy positive solutions of critical Schrödinger systems with mixed competition and cooperation terms: the higher dimensional case

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Regularity of all minimizers of a class of spectral partition problems

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Q5542608

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Neumann problems of semilinear elliptic equations involving critical Sobolev exponents

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Partial symmetry of vector solutions for elliptic systems

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Ground states of nonlinear Schrödinger systems with mixed couplings

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Nodal solutions to superlinear biharmonic equations via decomposition in dual cones

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On a $K$-component elliptic system with the Sobolev critical exponent in high dimensions: the repulsive case

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Q3275400

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Positive least energy solutions for $k$-coupled Schrödinger system with critical exponent: the higher dimension and cooperative case

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Normalized solutions to Schrödinger systems with linear and nonlinear couplings

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The estimates on the energy functional of an elliptic system with Neumann boundary conditions

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Identifiers

zbMATH Open document ID

1547.35007

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6592001