Solvability Of Several Classes Of Semilinear Elliptic Systems

Firstly,this paper briefly introduces the origin and development of partial differential equations,and some courses that I have learned in my graduate stage.The solvability of boundary value problems for Biharmonic Equations and the solvability of Semilinear Elliptic Systems in bounded ‘hole' domains are studied in this paper.The existence and uniqueness of positive solutions for biharmonic equation boundary value problems are proved.At the same time,the non-existence of solutions is explored.The existence and uniqueness of positive solutions for Semilinear Elliptic System Boundary Value Problems are proved.The methods used include fixed point theorem,Green identity,maximum principle,etc.