| Boundary blow-up elliptic problem exists in Riemannian geometry,mathematical physics equations,mathematical biology,population dynamics and other fields,the research on this problem promotes vigorous development in these fields,and continuously expand the scope of these fields,in turn,these fields have set a new challenge for the research of boundary blow-up problem.So it has great significance in theory and applications.In this thesis,we investigate the existence and uniqueness of solution to two types of elliptic boundary blow-up problems and obtain the asymptotic estimates results.The main contents of this thesis are as follows:The first chapter is the introduction.In this chapter,we briefly introduce the background,research status and main results of basic elliptical boundary blow-up problems.The research problems of this paper are described.Some symbols,definitions and theorems used in the research process are explained.In chapter 2,we study the existence,uniqueness and asymptotic estimates results of boundary blow-up solution to a class of elliptic equation with exponent,and prove the results in detail.In chapter 3,we study the existence,uniqueness and asymptotic estimates results of boundary blow-up solution to a class of elliptic equation with polynomial,and prove the results in detail.In chapter 4,the summary and the further study of this paper are given. |
