Non-existence of a secondary bifurcation point for a semilinear elliptic problem in the presence of symmetry

DOI10.1016/j.jmaa.2009.04.005zbMath1170.35425OpenAlexW2022712332MaRDI QIDQ1025815

Yasuhito Miyamoto

Publication date: 23 June 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.04.005

zbMATH Keywords

non-radially symmetric solutionno secondary bifurcationpresence of symmetrysemilinear elliptic Neumann problems

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Bifurcations in context of PDEs (35B32) Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) (35R20)

Related Items

Asymptotic transversality and symmetry breaking bifurcation from boundary concentrating solutions, Global branch from the second eigenvalue for a semilinear Neumann problem in a ball, Nondegeneracy of the second bifurcating branches for the Chafee-Infante problem on a planar symmetric domain, Global secondary bifurcation, symmetry breaking and period-doubling

Cites Work

• Global branches of non-radially symmetric solutions to a semilinear Neumann problem in a disk
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Instability results for reaction-diffusion equations with Neumann boundary conditions
• Nodal sets for ground states of Schrödinger operators with zero magnetic field in non simply connected domains
• Bifurcation theory. An introduction with applications of PDEs
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• On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations