Uniqueness of least energy solutions to a semilinear elliptic equation in \(\mathbb{R}^ 2\)

DOI10.1007/BF02567439zbMath0807.35043OpenAlexW1982882612MaRDI QIDQ1340217

Publication date: 9 March 1995

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155974

zbMATH Keywords

uniqueness semilinear elliptic equation mountain pass lemma bounded convex domain in \(\mathbb{R}^ 2\)Pokhozaev's identity solutions at the least energy

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Variational methods for second-order elliptic equations (35J20)

Related Items (43)

On the number of critical points of solutions of semilinear equations in ℝ2 ⋮ Uniqueness of extremals for some sharp Poincaré-Sobolev constants ⋮ Further remarks on the non-degeneracy condition ⋮ Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations ⋮ An energy-decreasing rearrangement of level sets preserving the domain and volume constraints ⋮ Rigorous Numerical Enclosures for Positive Solutions of Lane–Emden’s Equation with Sub-Square Exponents ⋮ Uniform a priori estimates for positive solutions of the Lane-Emden system in the plane ⋮ Uniqueness, multiplicity and nondegeneracy of positive solutions to the Lane-Emden problem ⋮ Concavity principles for nonautonomous elliptic equations and applications ⋮ Existence and orbital stability/instability of standing waves with prescribed mass for the \(L^2\)-supercritical NLS in bounded domains and exterior domains ⋮ Uniqueness of Nontrivial Solutions for Degenerate Monge–Ampere Equations ⋮ Concavity properties for solutions to \(p\)-Laplace equations with concave nonlinearities ⋮ Properties of solutions to a harmonic-mapping type equation with a Dirichlet boundary condition ⋮ Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods ⋮ The Cauchy-Dirichlet problem for the fast diffusion equation on bounded domains ⋮ Geometric properties of superlevel sets of semilinear elliptic equations in convex domains ⋮ A NOTE ON THE UNIQUENESS OF POSITIVE SOLUTIONS OF ROBIN PROBLEM ⋮ Some global results for a class of homogeneous nonlocal eigenvalue problems ⋮ On the lack of directional quasiconcavity of the fundamental mode in the clamped membrane problem ⋮ Symmetry and stability of asymptotic profiles for fast diffusion equations in annuli ⋮ Uniqueness of least energy solutions for Monge-Ampère functional ⋮ Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems ⋮ Sign-changing solutions for coupled Schrödinger equations with mixed coupling ⋮ Parabolic approach to nonlinear elliptic eigenvalue problems ⋮ Semilinear elliptic equations with the pseudo-relativistic operator on a bounded domain ⋮ Transition between nonlinear and linear eigenvalue problems ⋮ The shape of extremal functions for Poincaré-Sobolev-type inequalities in a ball ⋮ Existence of Multi-bump Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations ⋮ Sharp numerical inclusion of the best constant for embedding \(H_0^1(\Omega) \hookrightarrow L^p(\Omega)\) on bounded convex domain ⋮ Uniform a priori estimates for positive solutions of the Lane-Emden equation in the plane ⋮ Numerical verification method for positive solutions of elliptic problems ⋮ Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two ⋮ Asymptotic Estimates and Qualitative Properties of an Elliptic Problem in Dimension Two ⋮ Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains ⋮ A uniqueness result for a semilinear elliptic problem: a computer-assisted proof ⋮ Convergence rate of the finite element approximation for extremizers of Sobolev inequalities on 2D convex domains ⋮ A posteriori verification of the positivity of solutions to elliptic boundary value problems ⋮ Extremality conditions for the quasi-concavity function and applications ⋮ Numerical verification of positiveness for solutions to semilinear elliptic problems ⋮ The asymptotically linear Hénon problem ⋮ Stability of 2D steady Euler flows related to least energy solutions of the Lane-Emden equation ⋮ Positive solutions to the sublinear Lane-Emden equation are isolated ⋮ Asymptotic estimates for the least energy solution of a planar semi-linear Neumann problem

Cites Work

This page was built for publication: Uniqueness of least energy solutions to a semilinear elliptic equation in \(\mathbb{R}^ 2\)