Boundary Value Problems
Volume 2009 (2009), Article ID 540360, 8 pages
doi:10.1155/2009/540360
Existence of nontrivial solution for a nonlocal elliptic equation with nonlinear boundary condition
Fanglei Wang
and Yukun An
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Abstract
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.