The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions

In this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (Eλ,μ)(Eλ,μ) with 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)(λ,μ) belongs to a certain subset of R2R2.