Multiple Sign-Changing Solutions for Kirchhoff-Type Equations

We study the following Kirchhoff-type equations -(a + b integral(Omega)vertical bar del u vertical bar(2))Delta u + V(x)u = f(x, u), in Omega, u = 0, in partial derivative Omega, where Omega is a bounded smooth domain of R-N (N = 1, 2, 3), a > 0,b >= 0, f is an element of C((Omega) over bar x R, R), and V is an element of C((Omega) over bar, R). Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if f is odd with respect to its second variable, this problem has infinitely many sign-changing solutions.