The existence of infinitely many solutions of a class of nonlinear elliptic equations with Neumann boundary condition for both resonance and oscillation problems

Abstract

In this paper, we study and discuss nonlinear elliptic equations with Neumann boundary condition for both resonance and oscillation problem, and obtain new results on the exactly infinitely many positive and negative solutions, which are all nonconstant. The study of problem (1.1) are based on the variational methods and critical point theory. We prove the conclusion by using sub-sup solution method, Mountain Pass Theorem in order Intervals, Leray–Schauder degree theory and More theory.