The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system (Eλ,μ)(Eλ,μ) involving critical exponents and sign-changing weight functions. Using Nehari manifold, the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ)(λ,μ) belongs to a certain subset of R2R2.