关于一类非线性微分方程组的边值问题的渐近解(Ⅰ)

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On the Asymptotic Solutions of Boundary Value Problems for a Class of Systems of Nonlinear Differential Equations(Ⅰ)

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China

摘要: 应用新的方法,研究一类非线性微分方程组u"=v,εv"+f(x,u,u')v'-g(x,u,u')v=0(0<ε≤1),的边值问题的解的渐近性质.构造出解的渐近展开式,和估计了余项,改进并拓广了前人的工作.
- 非线性微分方程组 /
- 边值问题 /
- 渐近解
Abstract: A new method is applied to study the asymptotic behavior of solutions of boundnary value problems for a class of systems of nonlinear differential equations u"=v,εv"+f(x,u,u')v'-g(x,u,u')v=0(0<ε≤1).The asymptotic expansions of solutions are constructed,the remainders are estimated.The former works are improved and generalized.
- system of nonlinear differential equations /
- boundary value problem /
- asymptotic solution

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