Existence and multiplicity of positive solutions for Kirchhoff-Schrödinger-Poisson system with critical growth

This paper is concerned with the following Kirchhoff-Schrödinger-Poisson system: {[ - (a+ b∫ _ℝ^3|∇ u|^2dx )Δ u + V(x)u+ϕ u=λ g(x)u^q-1+h(x)u^5, in ℝ^3,; -Δϕ = u^2, u>0, in ℝ^3,; ]. where a>0 , b≥ 0 , q∈ [4,6) and λ >0 is a parameter. Under some suitable conditions on V ( x ), g ( x ) and h ( x ), by using the Nehari manifold technique and the Ljusternik-Schnirelmann category theory, we relate the number of positive solutions with the topology of the global maximum set of h when λ is small enough. Furthermore, with the aid of the Mountain Pass Theorem, we also obtain an existence result for λ sufficiently large. Recent results from the literature are generally improved and extended.