A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function

Abstract

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system ( E λ , μ ) involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters ( λ , μ ) belongs to a certain subset of R 2 .