The Nehari manifold for indefinite Kirchhoff problem with Caffarelli-Kohn-Nirenberg type critical growth

Abstract

In this paper we study the following class of nonlocal problems involving Caffarelli-Kohn-Nirenberg type critical growthwhere h(x) ≥ 0, f (x) is a continuous function which may change sign, λ, µ are positive real parameters and 1and the function M : R + ∪ {0} → R + is exactly as in the Kirchhoff model, given by M(t) = α + βt, α, β > 0. Using the idea of the constrained minimization on Nehari manifold we show the existence of at least two positive solutions for suitable choices of λ and µ.