Multiplicity and concentration of nontrivial solutions for Kirchhoff-Schrodinger-Poisson system with steep potential well

This article is about the following Kirchhoff-Schrodinger-Poisson system with steep potential well {-(a+b integral R-3|del u|(2)dx)triangle u + lambda V(x)u + mu phi(x)u = f(x,u)+h(x)|u|(alpha) in R-3, -triangle phi=u(2), in R-3, (1.1) where a,b,lambda > 0 are constants, mu > 0, and 0 < alpha < 1,f is an element of C(R(N)xR,R). By using the variational principle, we overcome the difficulties caused by Poisson's term and obtain system (1.1) that has two nontrivial solutions under certain assumptions. Moreover, we study the concentration of solutions and obtain new conclusions of system (1.1). Finally, we present the case where the solution to system (1.1) does not exist.