Abstract
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.
Citation
Anran Li. Hongrui Cai. Jiabao Su. "Quasilinear elliptic equations with singular potentials and bounded discontinuous nonlinearities." Topol. Methods Nonlinear Anal. 43 (2) 439 - 450, 2014.
Information