Ground states for nonlinear Kirchhoff equations with critical growth

Abstract

This paper is concerned with the existence, multiplicity and concentration behavior of positive solutions for the critical Kirchhoff-type problem (Formula presented.) where ε and λ are positive parameters, and a, b > 0 are constants, 2*(= 6) is the critical Sobolev exponent in dimension three, V is a positive continuous potential satisfying some conditions, and f is a subcritical nonlinear term. We use the variational methods to relate the number of solutions with the topology of the set where V attains its minimum, for all sufficiently large λ and small ε. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.