On The Multiplicity Of Solutions To A Class Of Semilinear Neumann Problems

In this paper, we study the multiplicity of the radial solutions to a class of semilinear supercritical elliptic Neumann problems. The main contents are organized as following:In chapter1, we state the background for our problems and the main work of this article.In chapter2, we give some preliminaries and some notations we needed.In chapter3, we consider existence of the radial solutions to a class of su-percritical problems with Neumann boundary condition. By variational technique and study of a suitable limit problem, we prove the existence of at least three radial solutions of this problem. Specifically, this problem can be stated as following: here, Ω is a annuli on RN and p is large enough. We prove that, when g(r)∈L1(a,b) satisfies g(r)>0a.e. in (a,b) and λ(r)∈L1(a,b) is positive increasing function in (a,b), then for every p large enough, problem (A) admits at least three distinct radial solutions.In chapter4, we consider the multiplicity of solutions to problem (A) with au-tonomous condition (g(|x|)=λ(|x|)). We can prove that when g(|x|)=λ(|x|)and λ(r)∈L1(a,b) is positive increasing function in (a, b), then for every p large enough, problem (A) has at least three distinct nonconstant radial solutions.