二阶非线性微分方程组三点边值问题解的存在性

Existence of Solution of Three Point Boundary Value Problem for the Nonlinear Differential Systems of Order 2

利用上下解方法及Schauder不动点定理,证明了二阶非线性微分方程组三点边值问题:y″=f(t,y,z,y′,z′)z″=g(t,y,z,y′,z′)y(-1)=A,y(1)=B,z(0)=C0,z′(0)=C1,解的存在性,并由此得到四阶非线性微分方程三点边值问题解的存在性,一定程度上推广了前人的一些结果[2],[3].作为文章结果的应用,讨论了奇摄动四阶半线性三点边值问题,得到该问题解的存在性及解的渐近估计.

In this paper, existence result of three point boundary value problem for the nonlinear differential system of order 2 is gained via the method of upper-lower solution and Schauder fixed point theorem {y＂=f（t,y,z,y＇,z＇） z＂=g（t,y,z,y＇,z＇） y（-1）=A,y（1）=B,z（0）=C0,z＇（0）=C1, Moreover, existence result of three point boundary value problem for forth-order nonlinear differential equation is directly gained by using the existence result aboved. As application of result in this paper, consider singular perturbed forth-order nonlinear three point boundary value problem, get its existence result and asymptotic esitmate of solution.