Abstract
We consider nonlinear boundary-value problems (with Noetherian operator in the linear part) for systems of ordinary differential equations in the neighborhood of generating solutions. By using the Lyapunov — Schmidt method, we establish conditions for the existence of solutions of these boundary-value problems and propose iteration algorithms for their construction.
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References
A. A. Boichuk, V. F. Zhuravlev, and A. M. Samoilenko, Generalized Inverse Operators and Noetherian Boundary-Value Problems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1995).
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A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods for the Investigation of Solutions of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1986).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 2, pp. 162–171, February, 1998.
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Boichuk, A.A. Nonlinear boundary-value problems for systems of ordinary differential equations. Ukr Math J 50, 186–195 (1998). https://doi.org/10.1007/BF02513444
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DOI: https://doi.org/10.1007/BF02513444