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
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
Copyright © 2006 Juan Wang and Chun-Lei Tang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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|.