Boundary Value Problems
Volume 2009 (2009), Article ID 540360, 8 pages
Research Article

Existence of Nontrivial Solution for a Nonlocal Elliptic Equation with Nonlinear Boundary Condition

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 15 December 2008; Accepted 17 February 2009

Academic Editor: Zhitao Zhang

Copyright © 2009 Fanglei Wang and Yukun An. 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.


In this paper, we establish two different existence results of solutions for a nonlocal elliptic equations with nonlinear boundary condition. The first one is based on Galerkin method, and gives a priori estimate. The second one is based on Mountain Pass Lemma.