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Quasilinear elliptic equations on \({\mathbb{R}^{N}}\) with singular potentials and bounded nonlinearity

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An Erratum to this article was published on 08 January 2012

Abstract

We study the existence and multiplicity of nontrivial radial solutions of the quasilinear equation

$$\left\{\begin{array}{ll}-{div}(|\nabla u|^{p-2}\nabla u)+V(|x|)|u|^{p-2}u=Q(|x|)f(u),\quad x\in \mathbb{R}^N,\\u(x) \rightarrow 0, \quad |x|\rightarrow \infty \end{array}\right.$$

with singular radial potentials V,Q and bounded nonlinearity f. The approaches used here are based on a compact embedding from \({W_r^{1,p}(\mathbb{R}^N; V)}\) into \({L^1(\mathbb{R}^N; Q)}\) and minimax methods. A uniqueness result is given for f ≡ 1.

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Authors and Affiliations

  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People’s Republic of China

    Jiabao Su

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  1. Jiabao Su
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Correspondence to Jiabao Su.

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Supported by NSFC-10831005, NSFB-1082004, KZ201010028027.

An erratum to this article can be found at http://dx.doi.org/10.1007/s00033-011-0186-4.

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Su, J. Quasilinear elliptic equations on \({\mathbb{R}^{N}}\) with singular potentials and bounded nonlinearity. Z. Angew. Math. Phys. 63, 51–62 (2012). https://doi.org/10.1007/s00033-011-0138-z

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