具有转向点的非线性向量问题的奇摄动

Singular Perturbation For Nonlinear Vector Problems with Turning points

本文利用微分不等式理论,借助文献的方法来讨论如下形式的非线性向量过值问题:■在适当的假设下,获得具有转向点的解的存在性及阶渐近估计.

In this paper, the nonlinear vector boundary value problems of the following forms are considered: εy'=f(t,y,y',z,ε),εz'=g(t,y,z,z',ε),y(a,ε)=A_1, y(b,ε)=B_1, where ε>0 is a small parameter, f and g are continuous functions in R^(?). There exist t_1 and t_2 (a<t_1<t_2<b) so that f_y, (t_1,y,y',z,ε)=g_(2')(t_2,y,z,z', ε)=0, that is, t_1 and t_2 are turning points. Under appropriate assumptions, by means of theory of differential inequalities, the existence of solutions of the above problems is proved and the zero-order asymptotic estimation of solution is obtained.