A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear neumann problems

Abstract

In this paper we present a framework which permits the unified treatment of the existence of multiple solutions for superlinear and sublinear Neumann problems. Using critical point theory, truncation techniques, the method of upper-lower solutions, Morse theory and the invariance properties of the negative gradient flow, we show that the problem can have seven nontrivial smooth solutions, four of which have constant sign and three are nodal.