摘要
In this paper, we study the existence of multiple solutions to the following nonlinear elliptic bound- ary value problem of p-Laplacian type：{-△pu=div（｜Du_p-2Du）is the p-Laplacian of u andin W1 0^p（Ω）but f（x,1）dose not satisfy the Ambrosetti-Rabinowitz condition. Under suitable assumptions onPass Theorem under（C）_ccondition. Our main result generalizes a result by N. S. Papageorgiou, E. M. Rochaand V. Staicu in 2008 （Calculus of Variations and Partial Differential Equations, 33： 199-230（2008）） and a result by G. B. Li and H. S. Zhou in 2002 （Journal of the London Mathematical Society, 65：123 138（2002））.
In this paper, we study the existence of multiple solutions to the following nonlinear elliptic bound- ary value problem of p-Laplacian type：{-△pu=div（｜Du_p-2Du）is the p-Laplacian of u andin W1 0^p（Ω）but f（x,1）dose not satisfy the Ambrosetti-Rabinowitz condition. Under suitable assumptions onPass Theorem under（C）_ccondition. Our main result generalizes a result by N. S. Papageorgiou, E. M. Rochaand V. Staicu in 2008 （Calculus of Variations and Partial Differential Equations, 33： 199-230（2008）） and a result by G. B. Li and H. S. Zhou in 2002 （Journal of the London Mathematical Society, 65：123 138（2002））.
基金
Supported in part by the National Natural Science Foundation of China under Grant No:11071095,Grant No.11371159
Program for Changjiang Scholars and Innovative Research Team in University#IRT13066
