Multiple Constant Sign and Nodal Solutions for Superlinear Elliptic Equations

Abstract

We consider semilinear elliptic problems with a superlinear right hand side nonlinearity, which however, need not satisfy the Ambrosetti-Rabinowitz condition. Using a combination of variational methods, with Morse theory (critical groups) and truncation techniques, we prove multiplicity theorems providing precise sign information for the solutions. We show that the problem can have seven and eight solutions, all with prescribed sign. © 2009, Division of Functional Equations, The Mathematical Society of Japan. All rights reserved.