Quasilinear elliptic equations with singular potentials and bounded discontinuous nonlinearities
Keywords
Quasilinear elliptic equation, Sobolev embedding, non-smooth critical point theorem, bounded discontinuous nonlinearityAbstract
In this paper we study the quasilinear equation $$ \cases - \text{div}(|\nabla u|^{p-2} \nabla u)+V(|x|)|u|^{p-2} u= Q(|x|)f(u), & x\in \mathbb{R}^N, \\ u(x)\rightarrow 0,\quad |x|\rightarrow \infty. \endcases \leqno(\text{P}) $$ 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.Downloads
Published
2016-04-12
How to Cite
1.
LI, Anran, CAI, Hongrui & SU, Jiabao. Quasilinear elliptic equations with singular potentials and bounded discontinuous nonlinearities. Topological Methods in Nonlinear Analysis [online]. 12 April 2016, T. 43, nr 2, s. 439–450. [accessed 7.2.2023].
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