## Topological Methods in Nonlinear Analysis

### Quasilinear elliptic equations with singular potentials and bounded discontinuous nonlinearities

#### Abstract

In this paper we study the quasilinear equation $$\begin{cases} - {\rm div}(|\nabla u|^{p-2} \nabla u)+V(|x|)|u|^{p-2} u= Q(|x|)f(u), & x\in \mathbb{R}^N, \\ u(x)\rightarrow 0,\quad |x|\rightarrow \infty. \end{cases} \tag{\rm P}$$ 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 43, Number 2 (2014), 439-450.

Dates
First available in Project Euclid: 11 April 2016

https://projecteuclid.org/euclid.tmna/1460381517

Mathematical Reviews number (MathSciNet)
MR3236979

Zentralblatt MATH identifier
1362.35140

#### Citation

Li, Anran; Cai, Hongrui; Su, Jiabao. Quasilinear elliptic equations with singular potentials and bounded discontinuous nonlinearities. Topol. Methods Nonlinear Anal. 43 (2014), no. 2, 439--450. https://projecteuclid.org/euclid.tmna/1460381517

#### References

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