The Existence Of Large Solutions For Smilinear Elliptic Equations

In this thesis, we discuss the existence and nonexistence of large solutions for semilinear elliptic equations by using the super-subsolution method, the maximum principle and the radial solutions method.The thesis is divided into four chapters.In the preface we state the background of this paper and the newest results.In chapter one we introduce some fundamental knowledge, which include the basic conditions and theorems. These theorems are important tools for the later work. We will directly use them and no longer prove them in this paper.In chapter two we mainly discuss the existence of large solutions for the semilinear elliptic equation The necessary and sufficient condition for the existence of large solutions is f,g satisfy in a bounded domain; and we also need p,q satisfy decline condition in RN.In chapter three we mainly discuss the existence of entire large solutions for the semilinear elliptic equation Δw+|▽w|=p(x)f(u)+q(x)g(u) in RN.We require f, g satisfy and p, q satisfy growth condition in RN.In chapter four we mainly discuss the large solutions for the semilinear elliptic equation We supply f,g satisfy the sublinear condition for the existence and nonexistence of large solutions in a bounded domain and RN.