The existence of positive solutions to an elliptic system with nonlinear boundary conditions
School of Mathematics and Statistics, Huazhong Normal University, Wuhan, 430079, P.R. China
Boundary Value Problems 2013, 2013:159 doi:10.1186/1687-2770-2013-159Published: 1 July 2013
In this paper, we consider the following system:
where Ω is a bounded domain in () with smooth boundary, is the outer normal derivative and are positive and continuous functions. Under certain assumptions on and , but without the usual (AR) condition, we prove that the problem has at least one positive strong pair solution (see Definition 1.4 below) by applying a linking theorem for strong indefinite functional.
MSC: 35A01, 35J20, 35J25.