Nondegeneracy of the second bifurcating branches for the Chafee-Infante problem on a planar symmetric domain

DOI10.1090/S0002-9939-2010-10616-0zbMath1211.35123MaRDI QIDQ3085061

Yasuhito Miyamoto

Publication date: 28 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

bifurcationsign-changing solutionsecond eigenvalueglobal branchplanar symmetric domain

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Second-order elliptic equations (35J15) Bifurcations in context of PDEs (35B32) Semilinear elliptic equations (35J61)

Cites Work

• Global branches of sign-changing solutions to a semilinear Dirichlet problem in a disk
• On the nodal lines of second eigenfunctions of the fixed membrane problem
• Global branches of non-radially symmetric solutions to a semilinear Neumann problem in a disk
• Non-existence of a secondary bifurcation point for a semilinear elliptic problem in the presence of symmetry
• Symmetry and related properties via the maximum principle
• Bifurcations caused by perturbing the domain in an elliptic equation
• Uniqueness of global positive solution branches of nonlinear elliptic problems
• Bifurcation from simple eigenvalues
• Remarks on the Second Eigenvalue of a Symmetric Simply Connected Plane Region
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Solution curves for semilinear equations on a ball
• Local bifurcation from the second eigenvalue of the Laplacian in a square
• On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations

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