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 .
© 1997 Rocky Mountain Mathematics Consortium
Castro, Alfonso; Cossio, Jorge; and Neuberger, John M., "A Sign-Changing Solution for a Superlinear Dirichlet Problem" (1997). All HMC Faculty Publications and Research. 480.