Boundary Value Problems 
Volume 2006 (2006), Article ID 47275, 12 pages
doi:10.1155/BVP/2006/47275

Existence and multiplicity of solutions for a class of superlinear p-Laplacian equations

Juan Wang and Chun-Lei Tang

 Department of Mathematics, School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Received 16 May 2006; Revised 5 July 2006; Accepted 6 July 2006

Abstract

By a variant version of mountain pass theorem, the existence and multiplicity of solutions are obtained for a class of superlinear p-Laplacian equations: −Δpu=f(x,u). In this paper, we suppose neither f satisfies the superquadratic condition in Ambrosetti-Rabinowitz sense nor f(x,t)/|t|p−1 is nondecreasing with respect to |t|.