Symmetry, degeneracy, and universality in semilinear elliptic equations. Infinitesimal symmetry-breaking

DOI10.1016/0022-1236(90)90099-7zbMath0702.35016OpenAlexW2079290455MaRDI QIDQ914948

J. A. Smoller, Arthur G. Wassermann

Publication date: 1990

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2027.42/28676

zbMATH Keywords

semilinear elliptic equationsradial solutionsLaplaciankerneleigenspaceasymmetric solutionslinearized operatorsinfinitesimal symmetry-breaking

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Bifurcations in context of PDEs (35B32)

Related Items (8)

Symmetry-breaking at non-positive solutions of semilinear elliptic equations ⋮ Morse index of layered solutions to the heterogeneous Allen-Cahn equation ⋮ Bifurcation and symmetry-breaking ⋮ Remarks on the uniqueness of radial solutions ⋮ On the monotonicity of the time-map ⋮ Radial and bifurcating non-radial solutions for a singular perturbation problem in the case of exchange of stabilities ⋮ Symmetry breaking of solutions of non-cooperative elliptic systems ⋮ Equivariant Bifurcation in Geometric Variational Problems

Cites Work

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• Existence, uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations
• Symmetry-breaking for solutions of semilinear elliptic equations with general boundary conditions
• An existence theorem for positive solutions of semilinear elliptic equations
• Symmetry-breaking for positive solutions of semilinear elliptic equations
• Existence of positive solutions for semilinear elliptic equations in general domains
• Topics in harmonic analysis on homogeneous spaces
• On Non-Radially Symmetric Bifurcation
• On Positive Solutions of Semilinear Elliptic Equations

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