STUDY OF SOLVABILITY OF BOUNDARY VALUE PROBLEMS FOR ONE SINGULAR DIFFERENTIAL EQUATION

A. V. Kungurtseva, I. A. Kolesnikov

Abstract


In this paper, the abstract theory of functional-differential equations is applied to some singular second-order differential equation, which is a generalization of equations encountered in the theory of chemical reactions. The result is based on the properties of the Green's operator of the corresponding linear problem.

Keywords


functional differential equations; quasilinear boundary value problems; linear equation; singular equation; unique solvability; well-defined solvability; finite-dimensional parametrizability; Green's operator.

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References


Azbelev N.V., Rakhmatullina L.F. [Abstract Functional-Differential Equations]. Functional-Differential Equations – Funkcional’no-Differencial’nye Uravneniya, Perm, 1987. – pp. 3–11. (in Russian)

Vasiliev A.V., Ermakov A.E., Kolosov S.V., Kolosov A.I. [On One Problem of the Theory of Chemical Reactions]. Matematicheskaya Fizika i Nelinejnaya Mekhanika – Mathematical Physics and Nonlinear Mechanics, 1987, no. 8, pp. 35–39. (in Russian)

Kungurtseva A.V. On a Class of Boundary Value Problems for Singular Equations. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 1995, no. 9, pp. 30–36. (in Russian)

Shekhter B.L. A Boundary Value Problem for a System of Ordinary Differential Equations. Differential Equations, 1982, vol. 18, no. 10, pp. 1707–1717. (in Russian)

Azbelev N.V., Maksimov V.P., Rakhmatullina L.F. [Introduction to the Theory of Functional-Differential Equations]. Moscow, Nauka publ., 1991.(in Russian)

Plaksina I.M. [To the Question of Fredholm and Solvability of One Singular Boundary Problem for the Functional Differential Equation]. Tambov University Reports. Series: Natural and Technical Sciences, 2011, vol. 16, issue 4, pp. 1150–1152.

Bravyi E.I. [Solvability of Edge Problems for Linear Functional-Differential Equations]. Moscow–Izhevsk, Regulyarnaya i Haoticheskaya Dinamika Publ., 2011. (in Russian)

Larionov A.S., Nikishina I.A. [Solvability of Nonlinear Problems for a First-order Functional Differential Equation]. Funkcional’no-Differencial’nye Uuravneniya: Teoriya i Prilozheniya: Materialy Konferencii, Posvyashchennoj 95-letiyu so Dnya Rozhdeniya Professora N.V. Azbeleva, Perm’, 17–19 Maya 2017. – Functional Differential Equations: Theory and Applications: Materials of a Conference Dedicated to the 95th Anniversary of the Birth of Professor N.V. Azbelev, Perm, May 17–19, 2017. Perm, Permskij nacional’nyj issledovatel’skij politekhnicheskij universitet Publ., 2018, – pp. 126–133. (in Russian)

Abdullaev A.R. [Surjectivity, as a Stable Property of Linear Operators]. Vestnik PGTU. Matematika i Prikladnaya matematika. – Bulletin of PSTU. Mathematics and applied mathematics, 1997, no. 4, pp. 35–43. (in Russian)

Maximov V.P. [On the Question of Parameterization of Many Solutions of the Functional-Differential Equation]. Funkcional’no-differencial’nye uravneniya: Mezhvuzovskij sbornik nauchnyh trudov. – Functional-Differential Equations: Intercollegiate Collection of ScientificWorks. Perm, Permskij politekhnicheskij institut Publ., 1988, pp. 14–20. (in Russian)

Weinberg M.M, Trenogin V.A. [Branching Theory of Solutions to Nonlinear Equations]. Moscow, Nauka publ., 1969. (in Russian)

Balandin A.S., Sabatulina T.L. Solvability of Autonomous Differential Equation with Aftereffect on Negative Semi-axis. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, no. 10, pp. 20–37. (in Russian)

Plaksina I.M. On Solvability of Singular Cauchy Problem for Functional-Differential Equation with Special Type Deviation. Tambov University Reports. Series: Natural and Technical Sciences, 2018, vol. 23, issue 123, pp. 539–546. doi: 10.20310/1810-0198-2018-23-123-539-546


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