Existence Of Solutions Of Semilinear Elliptic Systems

The existence and nonexistence of large solutions for the semilinear elliptic systems and are discussed in this paper, where Ω(?)Rn is either a smooth bounded domain or the whole space.The paper is divided into four parts.In the preface it state the background of this paper and the newest results.In chapter one we introduce some fundamental knowledge, which include the definition of some large solutions, some elliptic equation theorems, and so on. These are important tools for the later work. We will directely use them and without proof in this paper.In chapter two we discuss the existence and nonexistence of large solutions for the mixed sublinear/superilinear elliptic system by using the monotonicity principle and reduction method, we obtain sufficient conditions for the existence of radial large solutions of the system, the necessary and sufficient conditions for the existence of entire large solutions of the system. Moreover, the nonexistence of large solution of the system in Rn is proved.In chapter three we investigate the existence problem of solutions for semilinear elliptic system with gardient term We give the necessary and sufficient conditions which ensure the existence of entire large solutions and entire bounded solutions, and we also obtain some appropriate sufficient conditions for the nonexistence of the large solutions and entire large solutions. We find the influence of the coefficient to the solutions of the systems.