某类二阶非线性系统初值问题的奇摄动<sup>*</sup>

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某类二阶非线性系统初值问题的奇摄动^*

基金项目: *国家自然科学基金资助课题

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.
- 非线性系统 /
- 奇异摄动 /
- 多参数展开 /
- 对角化技巧
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.
- nonlinear system /
- singular perturbation /
- many-parameter expansion /
- technique of diagonalization

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[2]	Chang,K.W.,Singular perturbations of a general boundary value problem,SIAM,J Math.Anal.,3(1972),520-526.
[3]	林宗池,非线性系统边值问题的奇摄动,福建师大学报(自然科学版),5,4(1989),1-8.