Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3

We study the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem {-(epsilon(2)a +epsilon b integral vertical bar del u vertical bar(2)) + V (x) u = f (u) in R-3, u is an element of H-1 (R-3), u > 0 in R-3, where epsilon > 0 is a parameter and a, b > 0 are constants: V is a positive continuous potential satisfying some conditions and f is a subcritical nonlinear term. We relate the number of solutions with the topology of the set where V attains its minimum. The results are proved by using the variational methods. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.