摘要:
本文研究某类二阶非线性向量微分方程初值问题ε'x"=f(t,x,x',ε),x(0,ε)=a,x'(0,ε)=β的奇摄动,其中r>0为任意常数,ε>0为小参数,x,f,α,β∈Rn.在适当的假设下,利用多参数展开法和对角化技巧,证得摄动问题解的存在和导出解的高阶的一致有效渐近展开式.
Abstract:
In this paper,the singular perturbation of initial value problem for nonlinear second order vector differential equations ε'x"=f(i,x,x',ε) x(0,ε)=α,x'(0,ε)=β is discussed,where r>0 is an arbitrary constant,ε>0 is a small parameter,x,f,a and Under suitable assumptions,by using the method of many-parameter expansion and the technique of diagonalization,the existence oj the solution of perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.
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