Abstract
We use the method of a priori estimates to obtain effective sufficient solvability conditions for systems of nonlinear functional-differential equations with nonlinear boundary conditions of periodic type. The results are in a sense optimal.
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Kiguradze, I.T. and Puža, B., Theorems of Conti-Opial Type for Nonlinear Functional-Differential Equations, Differ. Uravn., 1997, vol. 33, no. 2, pp. 185–194.
Mukhigulashvili, S., On a Periodic Boundary Value Problem for Cyclic Feedback Type Linear Functional Differential Systems, Arch. Math., 2006, vol. 87, pp. 255–260.
Mukhigulashvili, S., On Periodic Solutions of Second Order Functional Differential Equations, Italian J. of Pure and Appl. Math., 2006, no. 20, pp. 29–50.
Kantorovich, L.V. and Akilov, G.P., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1977.
Kiguradze, I. and Puža, B., On Boundary Value Problems for Systems of Linear Functional Differential Equations, Czechoslovak Math. J., 1997, vol. 47, no. 2, pp. 341–373.
Conti, R., Problémes linéaires pour les équations différentielles ordinaires, Math. Nachr., 1961, vol. 23, no. 3, pp. 161–178.
Opial, Z.J., Linear Problems for Systems of Nonlinear Differential Equations, J. Differential Equations, 1967, vol. 3, no. 4, pp. 580–594.
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Original Russian Text © S.V. Mukhigulashvili, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 1, pp. 47–58.
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Mukhigulashvili, S.V. On a problem with nonlinear boundary conditions for systems of functional-differential equations. Diff Equat 46, 48–60 (2010). https://doi.org/10.1134/S0012266110010064
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DOI: https://doi.org/10.1134/S0012266110010064