Existence Of Positive Radial Solutions To Semilinear Elliptic Equations In Annular Domains

In this paper, the following two kinds of boundary value problems of semilinear elliptic partial differential equations will be considered:where 0<α<1,γ>1,Under a set of suitable hypotheses, with the aid of the super-subsolution method and the , the existence of solutions for these two kinds of boundary value problems of semilinear elliptic equations is given.The paper is divided into five chapters.The first chapter is an introduction of the whole paper. We talk about the background of this paper, and the plans for the research of the problem.The next chapter consists of some basic definitions and theorems, including the maximum,Green's function, and so on. They are the foundations and tools of the later work.The third and the forth chapters are the main part of this paper, where we discuss the exsistence of solutions by using the super-subsolution theorem and fixed point theorem , and we give the sufficient conditions for thepositive radial existence of solutions.In the last chapter, we summarize the work of whole paper and point out some open problems.