一类边值问题解的存在性及其奇异摄动

Solution's existence and singular perturbation for a class of boundary value problems

首先研究如下类型的边值问题:y″=f(t,y,y′)(a<t<b)py(a)-qy(b)=a,ry′(a)-sy′(b)=B的微分不等式与解的存在性.然后,利用所得的结果,研究二阶拟线性微分方程的边值问题εy″=f(t,y)y′+g(t,y)y(a)=y(b),ry′(a)-sy′(b)=B的奇异摄动现象.

At first, we study the theory of differential inequalities and existence of solution for the class of boundary value problems as following：y″=f（t,y,y′）（a〈t〈b）、py（a）-qy（b）=a,ry＇（a）-sy＇（b）=B Then using theresults obtained, the singular perturbation for boundary value problem of second order semilinear differential equation ：{εy″=f（t,y）y＇＋g（t,y）、y（a）=y（b）,ry＇（a）-sy＇（b）=B is explored.