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

Abstract

Abstract: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.