On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function

In this paper, we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign-changing weight function. With the help of the Nehari manifold, we prove that there are at least two positive solutions for Eq. (Eλ,f) in bounded domains.