奇摄动非线性系统边值问题<sup>*</sup>

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奇摄动非线性系统边值问题^*

基金项目: * 福建省自然科学基金

摘要: 本文利用对角化技巧和方法讨论二阶奇摄动非线性系统边值问题εy"＝f(t,y,y',ε),y(0,ε)＝α(ε),y(1,ε)＝b(ε)当Jacobi矩阵fy'的特征值有K个负实部和N－K个正实部时,解的存在性及其渐近性质。
- 非线性系统 /
- 边值问题 /
- 对角化 /
- 奇摄动
Abstract: In this paper, by the technique and the method of deagonalization, the boundary value problem for second order singularly perturbed nonlinear system as follows is dealt with:εy"=f(t,y,y',ε),y(0,ε)=a(ε),y(1,ε)=b(ε) The existance of the solution and its asymptotic properties are discussed when the eigenvaslues of Jacobi matrix fy' has K negative real parts and N-K positve real parts.
- nonlinear system /
- boundary value problem /
- diagonalization /
- singular perturbation

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