Multiple positive solutions for a class of Kirchhoff type problems involving critical Sobolev exponents

Abstract

In this paper, we study the multiplicity results of positive solutions for a class of Kirchhoff type problems involving critical growth terms. With the help of Nehari manifold and Ljusternik–Schnirelmann category theory, we investigate how the coefficient g(x) of the critical nonlinearity affects the number of positive solutions of that problem. Furthermore, we obtain a relationship between the number of positive solutions and the topology of the global maximum set of g.