INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH POWER NONLINEARITY

In this article we consider the Kirchhoff-type elliptic problem -(a + b integral(Omega)vertical bar del u vertical bar(2)dx)Delta u = vertical bar u vertical bar(p-2)u, in Omega, u = 0, on partial derivative Omega, where Omega is an element of R-N and p is an element of (2, 2*) with 2* = -2N/N-2 if N >= 3, and 2* = +infinity otherwise. We show that the problem possesses infinitely many sign-changing solutions by using combination of invariant sets of descent flow and the Ljusternik-Schnirelman type minimax method.