Positive and sign-changing solutions for Kirchhoff equations with indefinite potential

We deal with the nonlinear Kirchhoff problem -(a+b integral(R3)|del u|(2)dx)triangle u + V(x)u = f(u), x is an element of R-3, where a is a positive constant, b > 0 is a parameter, the potential function V is allowed to change its sign, and the nonlinearity f is an element of C(R,R) exhibits subcritical growth. Under some suitable conditions on V, we first prove that the problem has a positive ground state solution for all b > 0. Then, by using a more general global compactness lemma and a sign-changing Nehari manifold, combined with the method of constructing a sign-changing (PS)(c) sequence, we show the existence of a least energy sign-changing solution for b > 0 that is sufficiently small. Moreover, the asymptotic behavior b SE arrow 0 is established.