Three positive solutions for a semilinear elliptic equation in RNRN involving sign-changing weight

In this paper, we study the decomposition of the Nehari manifold via the combination of concave and convex nonlinearities. Furthermore, we use this result and the Lusternik–Schnirelmann category to prove that a semilinear elliptic equation in RNRN involving sign-changing weight function has at least three positive solutions.