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Existence and concentration of bound states for a Kirchhoff type problem with potentials vanishing or unbounded at infinity

In this paper, we study the existence and concentration behavior of positive solutions for the following Kirchhoff type equation: −(ɛ2a+ɛb∫R3|∇u|2dx)Δu+V(x)u=K(x)up,x∈R3,u∈H1(R3),u(x)>0, where ɛ is a positive parameter, a and b are positive constants, and 3 0 small. Furthermore, we show that the solution uɛ concentrates at the minimum points of A(s) as ɛ→0+.