| Abstract: | In this paper, we study the existence and concentration behavior of positive solutions for the following Kirchhoff type equation:  where ? is a positive parameter, a and b are positive constants, and 3<p<5. Let  denotes the ground energy function associated with  ,  , where  is regard as a parameter. Suppose that the potential V(x) decays to zero at infinity like |x|?α with 0<α≤2, we prove the existence of positive solutions u? belonging to  for vanishing or unbounded K(x) when ? > 0 small. Furthermore, we show that the solution u? concentrates at the minimum points of  as ?→0+. |
