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

This paper is concerned with the following Kirchhoff-Schrodinger-Poisson system: {-(a+b integral R3| backward difference u|2dx)Delta u+V(x)u+phi u=lambda g(x)uq-1+h(x)u5,inR3, {-Delta phi=u2,u>0 where a > 0, b = 0, q. [4, 6) and. > 0 is a parameter. Under some suitable conditions on V(x), g( x) and h(x), by using the Nehari manifold technique and the LjusternikSchnirelmann category theory, we relate the number of positive solutions with the topology of the global maximum set of h when. is small enough. Furthermore, with the aid of the Mountain Pass Theorem, we also obtain an existence result for. sufficiently large. Recent results from the literature are generally improved and extended.