Study On Boundary Value Problems Of A Kind Of Elliptic Equations

The research on solutions of differential equations has become a very active area in recently decades, because most differential equations come from the real problems in the abstract modeling. It is of great importance to study the solutions for differential equations. The research on the existence and uniqueness of second-order nonlinear equations is always so popular. Using different methods, people try to relax the conditions for the binding to prove. There are many methods to study this, such as variational method, homeomorphism method, semi group of operators etc. In this thesis, we discuss the existence and uniqueness for the solution of a nonlinear elliptic system. The study on elliptic equation can not be separated from ordinary differential equation theory as the basis. First, with 2-d Fourier transform, we prove that there can be at most one solution of a kind of elliptic equations by applying two elementary abstract algebraic lemmas. Second, under some weaker restrictions, we study the existence and uniqueness for the solution of the same equation by homeomorphism method.