A Sign-Changing Solution for a Superlinear Dirichlet Problem

We show that a superlinear boundary value problem has at least three nontrivial solutions.A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once.The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions.If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q.Wang [12].