Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem

DOI10.12775/TMNA.1999.020zbMath0958.35054OpenAlexW2546654582MaRDI QIDQ1577634

Shusen Yan, E. Norman Dancer

Publication date: 27 August 2000

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.12775/tmna.1999.020

zbMATH Keywords

nonlinearConley indexClarke derivativepeakssmall diffusion

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (13)

Boundary blow up solutions with a spike layer ⋮ Stable and finite Morse index solutions on 𝐑ⁿ or on bounded domains with small diffusion ⋮ Unnamed Item ⋮ On the existence of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds ⋮ Normalized multi-peak solutions to nonlinear elliptic problems ⋮ Multipeak solutions for an elliptic system of Fitzhugh-Nagumo type ⋮ Uniqueness of single-peaked solutions to singularity perturbed semilinear Dirichlet problems ⋮ SOLUTIONS WITH MULTIPLE ALTERNATE SIGN PEAKS ALONG A BOUNDARY GEODESIC TO A SEMILINEAR DIRICHLET PROBLEM ⋮ Nonexistence of multi-bubble solutions to some elliptic equations on convex domains ⋮ Nodal solutions for some singularly perturbed Dirichlet problems ⋮ Peak solutions without non-degeneracy conditions ⋮ Pointwise Blow-Up Phenomena for a Dirichlet Problem ⋮ A new type of concentration solutions for a singularly perturbed elliptic problem

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