Existence and Concentration of Solutions for a Class of Kirchhoff-Boussinesq Equation with Exponential Growth in R4

This paper is concerned with the existence and concentration of ground state solutions for the following class of elliptic Kirchhoff-Boussinesq type problems given by Delta(2)u +/-Delta(p)u+(1+lambda V(x))u=f(u) inR(4), where 2<p<4,f is an element of C(R,R)is a nonlinearity which has subcritical or critical exponential growth at infinity and V is an element of C(R-4,R)is a potential that vanishes on a bounded domain Omega subset of R-4.Using variational methods, we show the existence of ground state solutions, which concentrates on a ground state solution of a Kirchhoff-Boussinesq type equation in Omega.