Original scientific paper

Multiplicity of solutions for p-Laplacian equation in R^N with indefinite weight

Qing-Mei Zhou ; Library, Northeast Forestry University, Harbin, P.R. China
Ke-Qi Wang ; College of Mechanical and Electrical Engineering, Northea st Forestry University, Harbin,P. R. China

Abstract

In this article, we study the existence of infinitely many nontrivial solutions for a class of superlinear $p$-Laplacian equations
$$-\Delta_p u+V(x)|u|^{p-2}u=f(x,u),$$
where the primitive of the nonlinearity $f$ is of subcritical growth near $\infty$ in $u$ and the weight function $V$ is allowed to be sign-changing. Our results extend the recent results of Zhang and Xu [Q. Y. Zhang, B. Xu, {\em Multiplicity of solutions for a class of semilinear Schr\"{o}dinger equations with sign-changing potential}, J. Math. Anal. Appl {\bf 377}(2011), 834--840].

Keywords

p-Laplacian; Sign-changing potential; Superlinear problems; Variational method; Critical points

Hrčak ID:

149791

URI

https://hrcak.srce.hr/149791

Publication date:

18.12.2015.

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