Multiple solutions for p(x)-Laplacian type equations

Zigao Chen

ABSTRACT: We prove the existence of at least three weak solutions for the Dirichlet problem when the nonlinear term f is sublinear and p(x) is greater than n. This Dirichlet problem involves a general elliptic operator in divergence form (in particular, a p(x)-Laplace operator). Our method relies upon a recent critical point theorem obtained by Bonanno and Marano, and is combined with the theory of variable exponent Lebesgue-Sobolev spaces.

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College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011 China

* Corresponding author, E-mail: chenzigao@ncwu.edu.cn

Received 17 Oct 2012, Accepted 15 Oct 2013