Discussion On Boundary Value Problems Of Differential Equations

In this thesis,we investigate the solvability of differential equations by using the fixed point theorem,implicit function theorem,variation calculus theorem and so on.In passage 1,we discuss the solvability to Boundary Value Problems of a Semilinear Elliptic Equation system:According to f(x,s,t),g(x,s,t) with s,t are sublinear and superlinear in the infinity and zero point,the existence of solutions for two kinds of semilinear elliptic systems have been proved by using the fixed point theorem,and two concrete examples are given.In passage 2,we solve approximate solutions of differential equations by using the variation calculus theorem.Mainly introduces change problem approximate solution to the two classical methods: Riesz method,Galerkin method,and the two methods gives examples.