Critical points of a singular perturbation problem via reduced energy and local linking

DOI10.1006/jdeq.1999.3667zbMath0942.35078OpenAlexW2069677289MaRDI QIDQ1970029

Nicholas D. Alikakos, Michał Kowalczyk

Publication date: 12 July 2000

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3667

zbMATH Keywords

Neumann boundary value problemvariational methodsasymptotics of critical valuesnonlinear elliptic equation with parameter

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25) Variational methods applied to PDEs (35A15) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (11)

Standing waves in the FitzHugh-Nagumo system and a problem in combinatorial geometry ⋮ Existence and concentration of ground states of coupled nonlinear Schrödinger equations ⋮ Higher order energy expansions for some singularly perturbed Neumann problems. ⋮ Multiple spike layers in the shadow Gierer-Meinhardt system: Existence of equilibria and the quasi-invariant manifold ⋮ Existence and concentration of ground states of coupled nonlinear Schrödinger equations with bounded potentials ⋮ Approximately invariant manifolds and global dynamics of spike states ⋮ Nucleation in the FitzHugh-Nagumo system: Interface-spike solutions ⋮ On spikes concentrating on line-segments to a semilinear Neumann problem ⋮ Mixed weak-perturbative solution method for Maxwell's equations of diffusion with Müller's partial stress tensor in the low velocity limit ⋮ Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\) ⋮ Existence and instability of spike layer solutions to singular perturbation problems

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