A concentration phenomenon of the least energy solution to non-autonomous elliptic problems with a totally degenerate potential
| Autor: | Shun Kodama |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Dirichlet problem
Applied Mathematics 010102 general mathematics Degenerate energy levels Mathematics::Analysis of PDEs Boundary (topology) Geometry Function (mathematics) 01 natural sciences Omega 010305 fluids & plasmas Combinatorics Bounded function 0103 physical sciences Domain (ring theory) 0101 mathematics Analysis Energy (signal processing) Mathematics |
| Zdroj: | Communications on Pure and Applied Analysis. 16:671-698 |
| ISSN: | 1534-0392 |
| DOI: | 10.3934/cpaa.2017033 |
| Popis: | In this paper we study the following non-autonomous singularly perturbed Dirichlet problem: \begin{document}${\varepsilon ^2}\Delta u -u + K(x)f(u) = 0, \; u > 0\quad {\rm{in}}\; \Omega, \quad u = 0\quad {\rm{on}}\; \partial \Omega, $ \end{document} for a totally degenerate potential K. Here e > 0 is a small parameter, $\Omega \subset \mathbb{R}^N$ is a bounded domain with a smooth boundary, and f is an appropriate superlinear subcritical function. In particular, f satisfies $0 |
| Databáze: | OpenAIRE |
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