EXISTENCE AND CONCENTRATION OF GROUND STATE SOLUTIONS FOR A KIRCHHOFF TYPE PROBLEM

This article concerns the Kirchhoff type problem -(epsilon 2a+epsilon b integral R3 vertical bar del u vertical bar 2dx)Delta u+V(x) = K(x)vertical bar u vertical bar(p-1)u, x is an element of R-3, u is an element of H-1(R-3), where a,b are positive constants, 2 < p < 5, epsilon > 0 is a small parameter, and V(x), K(x) is an element of C-1(R-3). Under certain assumptions on the non-constant potentials V(x) and K(x), we prove the existence and concentration properties of a positive ground state solution as epsilon -> 0. Our main tool is a Nehari-Pohozaev manifold.