Existence of Positive Solutions to Semilinear Elliptic Systems Involving Concave and Convex Nonlinearities

In this paper, we studied the combined effect of concave and convex nonlinearities on the number of positive solutions for a semilinear elliptic system. We prove the existence of at least four positive solutions for a semilinear elliptic system involving concave and convex nonlinearities by using the Nehari manifold and the center mass function.