Properties Of Solutions To Two Semilinear Elliptic Problem

In this thesis,we study the existence and the regularity of positive classical solution and the existence of the large solutions for a singular semilinear elliptic Dirichlet problem and a semilinear elliptic value problem of second order with gradient terms.The thesis consists of three parts:In chapter l,the basic background, main studies, preliminaries, some methods are introduced.In chapter 2,I consider a class of semilinear elliptic equations:Where Ω is a bounded domain in R~N (N≥2) , and Using the super-sub solution method and the maximumprinciple,the existence result of posive classical solutions for a singular semilinear elliptic Dirichlet problem is obtained.I also established the regularity of classical solution to the above problem.In chaper 3, I consider a class of semilinear elliptic value problem, of second order with convection terms:Where Ω is a bounded domain in R~N (N≥3) , andUsing perturbed method and sub-supersolution method,the large solution is obtained.