Abstract and Applied Analysis
Volume 7 (2002), Issue 10, Pages 509-516

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

Copyright © 2002 Zhitao Zhang et al. 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.


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.