Mountain pass solutions for singularly perturbed nonlinear Dirichlet problems

DOI10.1016/j.jde.2005.07.008zbMath1154.35345OpenAlexW2062978884MaRDI QIDQ2575065

Jaeyoung Byeon

Publication date: 5 December 2005

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

Full work available at URL: https://doi.org/10.1016/j.jde.2005.07.008

zbMATH Keywords

Dirichlet problemsingular perturbationmountain pass solution

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20)

Related Items (9)

Singularly perturbed fractional Schrödinger equation involving a general critical nonlinearity ⋮ Standing waves for nonlinear Schrödinger equations involving critical growth ⋮ Solutions concentrating around the saddle points of the potential for two-dimensional Schrödinger equations ⋮ Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger-Moser type ⋮ Singularly perturbed nonlinear Dirichlet problems involving critical growth ⋮ Sign-changing semi-classical solutions of the Brezís-Nirenberg problems with jump nonlinearities in high dimensions ⋮ Singularly perturbed nonlinear Dirichlet problems with a general nonlinearity ⋮ Least energy sign-changing solutions of the singularly perturbed Brezis-Nirenberg problem ⋮ A concentration phenomenon of the least energy solution to non-autonomous elliptic problems with a totally degenerate potential

Cites Work

• Nonlinear scalar field equations. I: Existence of a ground state
• Symmetry and related properties via the maximum principle
• Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities
• Dual variational methods in critical point theory and applications
• Existence of large positive solutions of some nonlinear elliptic $si:equations on singularly perturbed doamins
• A Note on a Mountain Pass Characterization of Least Energy Solutions
• Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting
• A remark on least energy solutions in $\mathbf {R}^N$
• On the location and profile of spike‐layer solutions to singularly perturbed semilinear dirichlet problems
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