Symmetry breaking and Morse index of solutions of nonlinear elliptic problems in the plane

DOI10.1142/S021919971550087XzbMath1355.35080arXiv1308.0519OpenAlexW1480134734MaRDI QIDQ3188187

Sérgio L. N. Neves, Francesca Gladiali, Massimo Grossi

Publication date: 17 August 2016

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.0519

zbMATH Keywords

positive solutionsMorse indexnonradial solutionssemilinear elliptic problemssymmetry breakingbifurcation theory

Mathematics Subject Classification ID

Bifurcations in context of PDEs (35B32) Blow-up in context of PDEs (35B44) Positive solutions to PDEs (35B09) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items

A nonradial bifurcation result with applications to supercritical problems, A note on nonradial nodal solutions to the Henon problem in the disc, On some weighted fourth-order equations, Exact Morse index of radial solutions for semilinear elliptic equations with critical exponent on annuli, On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's, Quasi-radial solutions for the Lane-Emden problem in the ball, Exact Morse index computation for nodal radial solutions of Lane-Emden problems, Asymptotic profile and Morse index of the radial solutions of the Hénon equation, Nonradial solutions for the Hénon equation close to the threshold, The Hénon problem with large exponent in the disc, Morse index computation for radial solutions of the Hénon problem in the disk, A monotonicity result under symmetry and Morse index constraints in the plane, Monotonicity of the Morse index of radial solutions of the Hénon equation in dimension two

Cites Work

• Unnamed Item
• Unnamed Item
• Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity
• Global breaking of symmetry of positive solutions on two-dimensional annuli
• Perturbation theory for linear operators.
• Estimates on Pull-In Distances in Microelectromechanical Systems Models and Other Nonlinear Eigenvalue Problems
• NON-RADIAL GROUND STATES FOR THE HÉNON EQUATION
• Profile of Blow-up Solutions to Mean Field Equations with Singular Data
• Sur une classe de problemes non lineaires avec non linearite positive, croissante, convexe.
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains