A group-theoretical approach for nonlinear Schrödinger equations

DOI10.1515/ACV-2018-0016zbMath1454.49005OpenAlexW2883390355MaRDI QIDQ2216205

Giovanni Molica Bisci

Publication date: 15 December 2020

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv-2018-0016

zbMATH Keywords

variational methodsSchrödinger equationprinciple of symmetric criticalityradial and non-radial solutions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence theories for optimal control problems involving partial differential equations (49J20) Weak solutions to PDEs (35D30) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (5)

Existence and multiplicity of solutions for Schrödinger equations with sublinear nonlinearities ⋮ On nonlocal Dirichlet problems with oscillating term ⋮ Constrained local minima for smooth functionals and some consequences ⋮ Asymptotic behavior for non-autonomous fractional stochastic Ginzburg–Landau equations on unbounded domains ⋮ A bifurcation result for a Keller-Segel-type problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Infinitely many solutions for a perturbed Schrödinger equation
• On fractional Schrödinger equations in \({\mathbb R}^N\) without the Ambrosetti-Rabinowitz condition
• The principle of symmetric criticality
• Nonlinear scalar field equations. I: Existence of a ground state
• Infinitely many radial and non-radial solutions for a class of hemivariational inequalities
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation
• Ground state solutions of scalar field fractional Schrödinger equations
• Multiplicity of nonnegative solutions for quasilinear Schrödinger equations
• Symmetric mountain pass lemma and sublinear elliptic equations
• Functional analysis, Sobolev spaces and partial differential equations
• Symétrie et compacité dans les espaces de Sobolev
• On a class of nonlinear Schrödinger equations
• Existence of solitary waves in higher dimensions
• Infinitely many nonradial solutions of a Euclidean scalar field equation
• Infinitely many radial solutions of a semilinear elliptic problem on \(\mathbb{R}^ N\)
• Radial solutions of superlinear equations on \(\mathbb{R}^N\). I: A global variational approach
• Multiple solutions of differential equations without the Palais-Smale condition
• Minimax theorems
• A general variational principle and some of its applications
• Borderline gradient continuity of minima
• Harnack inequalities for double phase functionals
• Symmetry and multiple solutions for certain quasilinear elliptic equations
• A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
• Multiple existence of non-radial solutions with group invariance for sublinear elliptic equations
• Non-autonomous functionals, borderline cases and related function classes
• Sign Changing Solutions of Superlinear Schrödinger Equations
• Multiple Solutions of Nonlinear Scalar Field Equations
• Entire solutions to nonlinear scalar field equations with indefinite linear part
• Variational Methods for Nonlocal Fractional Problems
• Asymptotic states for equations of reaction and diffusion
• NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• A bifurcation result for non-local fractional equations
• A nonsmooth critical point theory approach to some nonlinear elliptic equations in \({\mathbb R}^n\)

This page was built for publication: A group-theoretical approach for nonlinear Schrödinger equations