Existence Of Explosive Solutions To Semilinear Elliptic Equations With Gradient Terms

In this paper, a kind of semilinear elliptic equation problemis considered, whereΩ(?) R~N(N≥3) is a C~2 domain, q∈[0,2],α>1-q.Under a set of suitable conditions, with the aid of the explosive super-subsolution method, some results on the existence of explosive solutions are obtained.The paper is divided into four sections.The first section 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 section consists of some basic definitions and theorems, including the maximum principle, Holder continuity, and so on. They are the foundations and tools of the later work.The third section is the main part of this paper, where we discuss the existence of solutions by using the super-subsolution theorem , and we give the sufficient conditions for the existence of solutions.At last, we summarize the work of the whole paper and point out some open problems.