Infinitely many sign-changing solutions for Kirchhoff type equations

In this paper, we study the Kirchhoff type equation - (a + b) integral(R3) vertical bar del u vertical bar(2) dx) Delta u + V(x) u = f (x, u), x epsilon R-3, u epsilon H-1(R-3), where a, b> 0 are constants and V(x) is a given positive potential. The nonlinearity covers the pure power type f (x, u) = Q(x)| u| p- 2u with 2< p< 4, a case in which few existence results of sign- changing solutions are known. By using the method of invariant sets of descending flow, we obtain a sign- changing solution for the given problem. Furthermore, if f is odd with respect to u, we prove that the problem admits infinitely many sign- changing solutions.