Three positive solutions for Dirichlet problems involving critical Sobolev exponent and sign-changing weight

Abstract 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–Schnirelman category to prove that a semilinear elliptic equation involving a sign-changing weight function has at least three positive solutions.

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