Abstract and Applied Analysis 
Volume 7 (2002), Issue 10, Pages 509-516
doi:10.1155/S1085337502207046

On an asymptotically linear elliptic Dirichlet problem

Zhitao Zhang, Shujie Li, Shibo Liu, and Weijie Feng

 Institute of Mathematics, Academy of Mathematics and Systems Sciences, Academia Sinica, Beijing 100080, China
Received 2 July 2002

Abstract

Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the boundness of the (PS) sequence of the corresponding functional. Moreover, the proof is very simple.