Quasilinear elliptic equations with singular potentials and bounded discontinuous nonlinearities
| Autor: | Jiabao Su, Hongrui Cai, Anran Li |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Measurable function Applied Mathematics 010102 general mathematics Mathematics::Analysis of PDEs Space (mathematics) Lipschitz continuity 01 natural sciences Critical point (mathematics) 010101 applied mathematics Bounded function Embedding Nabla symbol 0101 mathematics Analysis Mathematics |
| Zdroj: | Topol. Methods Nonlinear Anal. 43, no. 2 (2014), 439-450 |
| ISSN: | 1230-3429 |
| DOI: | 10.12775/tmna.2014.026 |
| Popis: | In this paper we study the quasilinear equation \begin{equation} \begin{cases} - {\rm div}(|\nabla u|^{p-2} \nabla u)+V(|x|)|u|^{p-2} u= Q(|x|)f(u), & x\in \mathbb{R}^N, \\ u(x)\rightarrow 0,\quad |x|\rightarrow \infty. \end{cases} \tag{$\rm P$} \end{equation} with singular radial potentials $V,Q$ and bounded measurable function $f$. The approaches used here are based on a compact embedding from the space $W^{1,p}_r(\mathbb{R}^N; V)$ into $L^1 (\mathbb{R}^N; Q)$ and a new multiple critical point theorem for locally Lipschitz continuous functionals. |
| Databáze: | OpenAIRE |
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