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Weakly nonlinear boundary-value problem in a special critical case

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We investigate the problem of the determination of conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems for systems of ordinary differential equations and the construction of these solutions. We consider the special critical case where the equation for finding the generating solution of a weakly nonlinear Noetherian boundary-value problem turns into an identity. We improve the classification of critical cases and construct an iterative algorithm for finding solutions of weakly nonlinear Noetherian boundary-value problems in the special critical case.

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Authors and Affiliations

  1. Slavyansk Pedagogic University, Slavyansk, Ukraine

    S. M. Chuiko

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  1. S. M. Chuiko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 4, pp. 548–562, April, 2009.

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Chuiko, S.M. Weakly nonlinear boundary-value problem in a special critical case. Ukr Math J 61, 657–673 (2009). https://doi.org/10.1007/s11253-009-0227-8

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  • DOI: https://doi.org/10.1007/s11253-009-0227-8

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