关于具有转向点的一类常微分方程的边值问题
On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points
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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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[1] Ackerberg,R.C.and O'Malley,R.E.Jr Boundary layer problem exhibiting resonance,Studies in Appl.Math.,49,3,(1970),277-295. [2] Grasman,J.,and Matkowsky,B.J.,A variational approach to singularly perturbed boundary value problems for ordinary and partial differential equations with turning points,SI AM I.Appl.Math.,32,3,(1977),588-597. [3] Nayfeh,A.H,,Perturbation Methods,Wiley,New York,(1973). [4] Cook,L.P and Eckhaus,W,,Resonance in a boundary value problem of singular perturbation type,Studies in A ppl.Math,,52.,2,(1973),129-139. [5] Matkowsky,B.J.,On boundary layer problem exhibiting resonance,SIAM Rev,17.1.(1975).82-100. -
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