关于常微分方程转点问题共振的必要条件*
On Necessary Conditions for Resonance in Turning Point Problems for Ordinary Differential Equations
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摘要: 本文首先修正带有转点的常微分方程共振必要条件中的一些误解,然后给出推导共振必要条件序列的递推过程.Abstract: In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has been offered.
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[1] Ackerberg,R, C, and R.E, O'Malley,Jr.,Boundary layer problem exhibiting resonance, Studies Appl.Math.,49,3(1970),277-295. [2] Wait,A.M.,A singular perturbation problem with a turning point, Bull.Austral.Math. Soc.,5(1971), 61-73. [3] Cook,L.P. and W. Eckhaus, Resonance in a boundary value problem of singular perturbation type,Studies in Appl.Math.,7,2 (1973),129-139. [4] Matkowsky,B, J.,On boundary layer problems exhibiting resonance, SIAM Rev.,17 (1975),82-100;Errata, Ibid.,18 (1976),112. [5] Olver, F.W, J.,Sufficient conditions for Ackerbergr O'Malley resonance,SIAM J. Math. Anal.,9(1978),328-355. -
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