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 and SU, Jiabao. Quasilinear elliptic equations with singular potentials and bounded discontinuous nonlinearities. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 43, no. 2, pp. 439 - 450. [Accessed 18 April 2024].
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