关于具有转向点的一类常微分方程的边值问题

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On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points

摘要: 本文应用多重尺度法研究具有转向点的一类常微分方程的边值问题.避免了[1]中出现的悖理,以及[2]中关于确定任意常数的变分运算;构造出边值问题的解的一致有效渐近近似式.并研究了非共振的情形.

Abstract: In this paper we study the boundary value problems for a class of ordinary differential equations with turning points by the method of multiple scales.The paradox in[1] and the variational approach in [2] are avoided,The uniformly valid asymptotic approximations of solutions have been constructed.We also study the case which does not exhibit resonance.

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