一阶系统非线性边值问题的奇摄动*
Singular Perturbation for a Nonlinear Boundary Value Problem of First Order System
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摘要: 本文应用比较定理研究了一类非线性边界条件的向量非线性奇摄动问题εx='f(t,x,y,e)εy'=g(t,x,y,ε)x(0)=A(ξ1,ξ2,x(1)-x(0),y(1)-y(0),ε)y(0)=B(ξ1,ξ,x(1)-x(0),y(1)-y(0),ε)这里ξ1,ξ2为ε的函数。0<ε<<1,在适当的条件下,作出了任意次精度的渐近展式。并得出余项估计。Abstract: In this paper, we study the following perturbed nonlinear boundary value problem of the form:εx'=f(t,x,y,ε)εy'=g(t,x,y,ε)x(0)= A(ξ1,ξ2,x(1) -x(0),y(1)- y(0),ε)y(0)=B(ξ1, ξ2,x(1)-x(0),y(1)-g(0),ε) where ξ1, ξ2 are functions of ε. 0<ε<<1. Under some suitable conditions, we give the asymptotic expansion of solution of any order, and obtain the estimation of remaindet term by using the comparison theorem.
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