Sign-changing solutions for Kirchhoff-type equations with indefinite nonlinearities

We are interested in the existence of sign-changing solutions for the following Kirchhoff-type equation {- (a + b integral(Omega) vertical bar del u|(2)dx) Delta u = (h(+)(x) +lambda h(-) (x)) vertical bar u vertical bar(p-2)u, x is an element of Omega, u = 0, x is an element of partial derivative Omega, where a, b > 0, Omega subset of R-3 is a bounded domain with smooth boundary, the potential h : (Omega) over bar -> R is a sign-changing continuous function, and lambda > 0 is a parameter. If p is an element of (4, 6), we prove the existence of least energy sign-changing solution u(b,lambda), the asymptotic behavior of u(b,lambda) as b -> 0(+) or -> +infinity are also analyzed. Moreover, if the set {x is an element of Omega : h(x) > 0} possesses several disjoint components, we also prove the existence of multi-bump sign-changing solutions.