Solutions concentrating at curves for some singularly perturbed elliptic problems

DOI10.1016/j.crma.2004.03.023zbMath1081.35044OpenAlexW2087240963MaRDI QIDQ1876849

Andrea Malchiodi

Publication date: 20 August 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.03.023

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25)

Related Items (14)

On Ambrosetti-Malchiodi-Ni conjecture on two-dimensional smooth bounded domains: clustering concentration layers ⋮ Concentration on curves for a Neumann Ambrosetti-Prodi-type problem in two-dimensional domains ⋮ On Ambrosetti-Malchiodi-Ni Conjecture on two-dimensional smooth bounded domains ⋮ Concentration phenomena of solutions for some singularly perturbed elliptic equations ⋮ Existence and concentration of positive solutions for a system of coupled saturable Schrödinger equations ⋮ Concentration on surfaces for a singularly perturbed Neumann problem in three-dimensional domains ⋮ An optimal bound on the number of interior spike solutions for the Lin-Ni-Takagi problem ⋮ Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions ⋮ Transition layer for the heterogeneous Allen-Cahn equation ⋮ Nonlinear Schrödinger equation: concentration on circles driven by an external magnetic field ⋮ LAYERED SOLUTIONS WITH CONCENTRATION ON LINES IN THREE-DIMENSIONAL DOMAINS ⋮ Nonlinear Schrödinger equations: concentration on weighted geodesics in the semi-classical limit ⋮ On the number of interior peak solutions for a singularly perturbed Neumann problem ⋮ Concentration on curves for nonlinear Schrödinger Equations

Cites Work

• Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains
• Foliations by constant mean curvature tubes
• Large amplitude stationary solutions to a chemotaxis system
• Locating the peaks of least-energy solutions to a semilinear Neumann problem
• Semi-classical states for nonlinear Schrödinger equations
• Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. I
• On a class of solutions with non-vanishing angular momentum for nonlinear Schrödinger equations
• Multiple clustered layer solutions for semilinear Neumann problems on a ball
• Multidimensional boundary layers for a singularly perturbed Neumann problem
• Nonexistence of single blow-up solutions for a nonlinear Schrödinger equation involving critical Sobolev exponent
• On the shape of least‐energy solutions to a semilinear Neumann problem
• On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems
• Semilinear Neumann boundary value problems on a rectangle
• Boundary concentration phenomena for a singularly perturbed elliptic problem
• Stable and finite Morse Index solutions on R^n or on bounded domains with small diffusion II
• Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, Part II
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