Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)

From MaRDI portal

Publication:1117397

Jump to:navigation, search

DOI10.1007/BF00275874zbMath0667.35023MaRDI QIDQ1117397

Kevin McLeod, James Serrin

Publication date: 1987

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problem uniqueness smooth solutions positive classical solutions exterior Neumann problem radial

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear boundary value problems for linear elliptic equations (35J65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items

Uniqueness of sign-changing radial solutions for \(\Delta u-u+| u|^{p-1}u=0\) in some ball and annulus, Further results on quasiperiodic partially localized solutions of homogeneous elliptic equations on \(\mathbb{R}^{N + 1} \), Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials, Uniqueness and nondegeneracy of positive radial solutions of \(\operatorname{div}(\rho\nabla u)+\rho (-gu+hu^p)=0\), On the exterior Dirichlet problem for \(\Delta u-u+f(x,u)=0\), Uniqueness results for Emden-Fowler boundary value problems, The mass concentration phenomenon for \(L^2\)-critical constrained problems related to Kirchhoff equations, Non-degeneracy of positive solutions of Kirchhoff equations and its application, Singular solutions of the elliptic equation \(\Delta u- u+u^ p =0\), On positive solutions of integral equations with the weighted Bessel potentials, Uniqueness theorems for negative radial solutions of \(k\)-Hessian equations in a ball, New singular standing wave solutions of the nonlinear Schrödinger equation, Positive solutions for a class of boundary value problems on infinite intervals, Uniqueness of positive radial solutions for quasilinear elliptic equations in an annulus, On precise center stable manifold theorems for certain reaction-diffusion and Klein-Gordon equations, Uniqueness of the ground state solutions of △u+f(u)=0 in Rⁿ, n≥3, Scattering for a nonlinear Schrödinger equation with a potential, Ground state energy of the two-component charged Bose gas, Positive solutions for nonlinear Schrödinger-Poisson systems with general nonlinearity, Un résultat de non-existence de solution positive pour une équation elliptique. (A nonexistence result for positive solutions of an elliptic equation), Oscillatory radial solutions of semilinear elliptic equations, Uniqueness of positive ground state solutions of the logarithmic Schrödinger equation, Existence of the vortex solutions of some semilinear elliptic equations, Eigenvalue problem for a \(p\)-Laplacian equation with trapping potentials, Uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball, Uniqueness of positive radial solutions of the Dirichlet problems \(-\Delta u=u^ p\pm u^ q\) in an annulus, Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\), Uniqueness and nondegeneracy of ground states for nonlinear Schrödinger equations with attractive inverse-power potential, Uniqueness of ground states for combined power-type nonlinear scalar field equations involving the Sobolev critical exponent at high frequencies in three and four dimensions, Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\), Dispersive estimates for matrix and scalar Schrödinger operators in dimension five, Blow-up behavior of ground states for a nonlinear Schrödinger system with attractive and repulsive interactions, Property of solutions for elliptic equation involving the higher-order fractional Laplacian in \(\mathbb{R}^n_+\), A critical center-stable manifold for Schrödinger's equation in three dimensions, On the spectrum of a mixed-type operator with applications to rotating wave solutions, Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities for high frequencies, A computer assisted study of uniqueness of ground state solutions, Existence and blow-up of attractive Gross-Pitaevskii minimizers with general bounded potentials, Blow-up profile of the focusing Gross-Pitaevskii minimizer under self-gravitating effect, Multiple normalized standing-wave solutions to the scalar non-linear Klein-Gordon equation with two competing powers, Radial solutions of \(\Delta u+f(u)=0\) with prescribed numbers of zeros, ON THE UNIQUENESS OF POSITIVE SOLUTIONS OF A QUASILINEAR EQUATION CONTAINING A WEIGHTED p-LAPLACIAN, THE SUPERLINEAR CASE, A generalized Pohožaev identity and uniqueness of positive radial solutions of \(\Delta u+g(r)u+h(r)u^p=0\), Uniqueness and nondegeneracy for some nonlinear elliptic problems in a ball., On the mass concentration for Bose-Einstein condensates with attractive interactions, On the Kolodner-Coffman method for the uniqueness problem of Emden-Fowler BVP, Uniqueness of the ground state solutions of quasilinear Schrödinger equations, The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications, Liouville's theorem for a fractional elliptic system, Orbital stability of standing waves for semilinear wave equations with indefinite energy, Uniqueness of positive radial solutions of \(\Delta{} u + g(r)u + h(r)u^ p = 0\) in \(\mathbb{R}{}^ n\), Stability estimates for the lowest eigenvalue of a Schrödinger operator, A centre-stable manifold for the focussing cubic NLS in \({\mathbb{R}}^{1+3\star}\), Properties of ground states of nonlinear Schrödinger equations under a weak constant magnetic field, On the existence of multipeaked solutions to a semilinear Neumann problem, On an inequality of Trudinger type and its application to a nonlinear Schrödinger equation, Mass concentration and local uniqueness of ground states for \(L^2\)-subcritical nonlinear Schrödinger equations, Uniqueness of radially symmetric positive solutions for \(- \Delta u+u=u^p\) in an annulus, Uniqueness and non-degeneracy for a nuclear nonlinear Schrödinger equation, Multiplicity results for sign changing bound state solutions of a semilinear equation, Nonexistence of solutions for indefinite fractional parabolic equations, Classification of solutions to a nonlocal equation with doubly Hardy-Littlewood-Sobolev critical exponents, Uniqueness of solutions to singular \(p\)-Laplacian equations with subcritical nonlinearity, Blow-up behavior of ground states of semilinear elliptic equations in \(R^ n\) involving critical Sobolev exponents, ON AXISYMMETRIC TRAVELING WAVES AND RADIAL SOLUTIONS OF SEMI-LINEAR ELLIPTIC EQUATIONS, Uniqueness and nondegeneracy of positive solutions of \((-\Delta )^su+u= u^p\) in \(\mathbb R^N\) when s is close to 1, Monotonicity properties for ground states of the scalar field equation, Monotonicity and symmetry of solutions to fractional Laplacian equation, Symmetry breaking for a class of semilinear elliptic problems and the bifurcation diagram for a 1-dimensional problem, Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. II, Radial oscillatory solutions of some quasi-linear elliptic equations, An integral equation involving Bessel potentials on half space, On uniqueness for nonlinear elliptic equation involving the Pucci's extremal operator, On the structure of positive solutions to an elliptic problem arising in thin film equations, On the uniqueness of sign changing bound state solutions of a semilinear equation, Minimal Energy Solutions and Infinitely Many Bifurcating Branches for a Class of Saturated Nonlinear Schrödinger Systems, Qualitative properties of ground states for singular elliptic equations with weights, A Liouville theorem for a class of fractional systems in \(\mathbb{R}_+^n\), Existence and non-existence of minimizers for Poincaré-Sobolev inequalities, The structure of solutions to the pseudo-conformally invariant nonlinear Schrödinger equation, The properties of solution for quasilinear elliptic equations, Optimal concentration for \(\mathrm{SU}(1,1)\) coherent state transforms and an analogue of the Lieb-Wehrl conjecture for \(\mathrm{SU}(1,1)\), Existence, localization and multiplicity results for positive radial solutions of semilinear elliptic systems, Radial solutions of an elliptic equation with singular nonlinearity, On the existence of multiple, single-peaked solutions for a semilinear Neumann problem, Symmetry of solutions to semilinear equations involving the fractional Laplacian, Exact multiplicity of positive solutions for a class of semilinear problems, Ground state of the mass-critical inhomogeneous nonlinear Schrödinger functional, Exact multiplicity of positive solutions for a class of semilinear problem. II, A note on the uniqueness and the non-degeneracy of positive radial solutions for semilinear elliptic problems and its application, Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential, Properties of the least action level, bifurcation phenomena and the existence of normalized solutions for a family of semi-linear elliptic equations without the hypothesis of autonomy, Existence and uniqueness of fast decay entire solutions of quasilinear elliptic equations, On the uniqueness of the second bound state solution of a semilinear equation, Solitary wave dynamics in an external potential, Vortex collapse for the L2-critical nonlinear Schrödinger equation, Qualitative analysis on logarithmic Schrödinger equation with general potential, Localized and expanding entire solutions of reaction-diffusion equations, Mixed problem for a cubic Schrödinger evolution equation with a cubic dissipative term, Uniqueness of positive radial solutions for \(\Delta u-u+u^p=0\) on an annulus., The Lieb–Thirring inequalities: Recent results and open problems, Semilinear elliptic problems with singular potentials in ℝ^N, Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with “rich” topology, Multiplicity results for ground state solutions of a semilinear equation via abrupt changes in magnitude of the nonlinearity, On some nonlinear Schrödinger equations in ℝ^N, Constructive proofs for localised radial solutions of semilinear elliptic systems on Rd, On the unboundedness of the number of solutions of a Dirichlet problem, Uniqueness, symmetry and convergence of positive ground state solutions of the Choquard type equation on a ball, Blow-up profile of Bose-Einstein condensate with singular potentials, Normalized multi-peak solutions to nonlinear elliptic problems, Existence of positive solutions for Kirchhoff-type problem in exterior domains, Shooting method for vortex solutions of a complex-valued Ginzburg–Landau equation, Uniqueness of a Minimizer for a Variational Problem Related to the Dispersion Managed Nonlinear Schrödinger Equation, Local Uniqueness and Refined Spike Profiles of Ground States for Two-Dimensional Attractive Bose-Einstein Condensates, About the number of positive solutions of Neumann problems, Ground states of two-component attractive Bose-Einstein condensates II: Semi-trivial limit behavior, Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials, Focusing nonlinear schrödinger equation and wave-packet collapse, Uniqueness of positive radial solutions for semilinear elliptic equations on annular domains, The existence and uniqueness of bound-state solutions of a semi-linear equation, Uniqueness of Radial Solutions of Semilinear Elliptic Equations, Existence of Positive Nonradial Solutions for Nonlinear Elliptic Equations in Annular Domains, Existence and uniqueness of monotone nodal solutions of a semilinear Neumann problem, Uniqueness of positive radial solutions of Δu+f(u,|xz.sfnc;)=0, Unnamed Item, Existence and Stability of Schrödinger Solitons on Noncompact Manifolds, Uniqueness of standing-waves for a non-linear Schrödinger equation with three pure-power combinations in dimension one, Local properties of solutions of a differential equation via normed linear spaces, On Uniqueness for the Generalized Choquard Equation, On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations, Uniqueness of positive radial solutions of semilinear elliptic equations in R^Nand séré's non—degeneracy condition

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1117397&oldid=13159387"