Uniqueness and critical spectrum of boundary spike solutions

DOI10.1017/S0308210500001487zbMath1112.35304OpenAlexW2170135299MaRDI QIDQ2784208

Wei, Juncheng

Publication date: 17 April 2002

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500001487

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Singular perturbations in context of PDEs (35B25)

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Existence and stability analysis of asymmetric patterns for the Gierer--Meinhardt system ⋮ Stable boundary spike clusters for the two-dimensional Gierer-Meinhardt system ⋮ Exact multiplicity results for a singularly perturbed Neumann problem ⋮ Approximately invariant manifolds and global dynamics of spike states ⋮ Stability of least energy patterns of the shadow system for an activator-inhibitor model. ⋮ The Gierer-Meinhardt system on a compact two-dimensional Riemannian manifold: Interaction of Gaussian curvature and Green's function ⋮ Orbital stability of bound states of nonlinear Schrödinger equations with linear and nonlinear optical lattices ⋮ Stable spike clusters on a compact two-dimensional Riemannian manifold ⋮ Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions ⋮ Mean field equations on tori: existence and uniqueness of evenly symmetric blow-up solutions ⋮ Existence and instability of spike layer solutions to singular perturbation problems ⋮ Multi-bump ground states of the Gierer-Meinhardt system in \(\mathbb R^2\).

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