Anti-symmetric Sign-changing Solutions of a Class of Fourth-orderBoundary Value Problems

The existence of anti-symmetric sign-changing solution for a nonlinear fourth-order boundary value problem is proved by use of Krasnosel`skii fixed point theorem and the continuation techniques of the solution when the non-linear terms meet certain assumed conditions. And through further generalization, the conditions, under which such fourth-order boundary value problems have multiple anti-symmetric sign-changing solutions, were worked out.