Open AccessNONSINGULAR INTEGRO-DIFFERENTIAL BOUNDARY VALUE PROBLEM NOT SOLVED WITH RESPECT TO THE DERIVATIVE
Author(s) -
С. М. Чуйко,
O. V. Chuiko,
V. O. Kuzmina
Publication year - 2020
Publication title -
bukovinsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 2309-4001
DOI - 10.31861/bmj2020.02.12
Subject(s) - mathematics , boundary value problem , invertible matrix , boundary (topology) , algebraic number , mathematical analysis , value (mathematics) , pure mathematics , algebraic equation , nonlinear system , physics , statistics , quantum mechanics
The study of the dierential-algebraic boundary value problems was established in thepapers of K. Weierstrass, M.M. Lusin and F.R. Gantmacher. Works of S. Campbell, Yu.E.Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, M.O. Perestyuk, V.P. Yakovets, O.A. Boi-chuk, A. Ilchmann and T. Reis are devoted to the systematic study of dierential-algebraicboundary value problems. At the same time, the study of dierential-algebraic boundary-valueproblems is closely related to the study of linear boundary-value problems for ordinary di-erential equations, initiated in the works of A. Poincare, A.M. Lyapunov, M.M. Krylov, N.N.Bogolyubov, I.G. Malkin, A.D. Myshkis, E.A. Grebenikov, Yu.A. Ryabov, Yu.A. Mitropolsky,I.T. Kiguradze, A.M. Samoilenko, M.O. Perestyuk and O.A. Boichuk.The study of the linear dierential-algebraic boundary value problems is connected withnumerous applications of corresponding mathematical models in the theory of nonlinear osci-llations, mechanics, biology, radio engineering, the theory of the motion stability. Thus, theactual problem is the transfer of the results obtained in the articles and monographs of S.Campbell, A.M. Samoilenko and O.A. Boichuk on the linear boundary value problems for theintegro-dierential boundary value problem not solved with respect to the derivative, in parti-cular, nding the necessary and sucient conditions of the existence of the desired solutions ofthe linear integro-dierential boundary value problem not solved with respect to the derivative.In this article we found the conditions of the existence and constructive scheme for ndingthe solutions of the linear Noetherian integro-dierential boundary value problem not solvedwith respect to the derivative. The proposed scheme of the research of the nonlinear Noetherianintegro-dierential boundary value problem not solved with respect to the derivative in thecritical case in this article can be transferred to the seminonlinear integro-dierential boundaryvalue problem not solved with respect to the derivative.