On the Regularization of a Linear Fredholm Boundary-Value Problem by a Degenerate Pulsed Action

Чуйко, С. М.

doi:10.1007/s10958-014-1710-9

Cited by 9 publications

(3 citation statements)

References 8 publications

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“…The results obtained, similarly [1,2,9,10,11,12] can be used in the theory of nonlinear Noetherian boundary value problems for systems of dierence-algebraic equations. In the case of insolvability, the dierence-algebraic boundary value problems can be regularized analogically to [13,14,15]. In addition, the results obtained similarly to [16]…”

Section: Reduction Of a Dierence-algebraic Boundary Value Problem To mentioning

confidence: 99%

Boundary value problems for systems of non-degenerate difference-algebraic equations

2019

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The study of differential-algebraic boundary value problems was initiated in the works of K. Weierstrass, N.N. Luzin and F.R. Gantmacher. Systematic study of differential-algebraic boundary value problems is devoted to the work of S. Campbell, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, M.O. Perestyuk, V.P. Yakovets, O.A. Boichuk, A. Ilchmann and T. Reis. The study of the differential-algebraic boundary value problems is associated with numerous applications of such problems in the theory of nonlinear oscillations, in mechanics, biology, radio engineering, theory of control, theory of motion stability. At the same time, the study of differential algebraic boundary value problems is closely related to the study of boundary value problems for difference equations, initiated in A.A. Markov, S.N. Bernstein, Ya.S. Besikovich, A.O. Gelfond, S.L. Sobolev, V.S. Ryaben'kii, V.B. Demidovich, A. Halanay, G.I. Marchuk, A.A. Samarskii, Yu.A. Mitropolsky, D.I. Martynyuk, G.M. Vayniko, A.M. Samoilenko, O.A. Boichuk and O.M. Stanzhitsky. Study of nonlinear singularly perturbed boundary value problems for difference equations in partial differences is devoted to the work of V.P. Anosov, L.S. Frank, P.E. Sobolevskii, A.L. Skubachevskii and A. Asheraliev. Consequently, the actual problem is the transfer of the results obtained in the articles by S. Campbell, A.M. Samoilenko and O.A. Boichuk on linear boundary value problems for difference-algebraic equations, in particular finding the necessary and sufficient conditions for the existence of the desired solutions, and also the construction of the Green's operator of the Cauchy problem and the generalized Green operator of a linear boundary value problem for a difference-algebraic equation. The solvability conditions are found in the paper, as well as the construction of a generalized Green operator for the Cauchy problem for a difference-algebraic system. The solvability conditions are found, as well as the construction of a generalized Green operator for a linear Noetherian difference-algebraic boundary value problem. An original classification of critical and noncritical cases for linear difference-algebraic boundary value problems is proposed.

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Section: Reduction Of a Dierence-algebraic Boundary Value Problem To mentioning

confidence: 99%

Boundary value problems for systems of non-degenerate difference-algebraic equations

2019

MAMM

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“…Особенностью задачи Коши (1) для дифференциально-алгебраических уравнений [6,7,8] [13,14]. Поставим следующую задачу: для каких классов задача Коши (1) имеет единственное решение при произвольных α, β, γ, δ…”

Section: постановка задачиunclassified

A сondition for the existence of a unique equilibrium position of the Cauchy problem for linear matrix differential algebraic equations

2017

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“…Òàêèì îáðàçîì, ïîñòàâëåííàÿ çàäà÷à ðàâíîñèëüíà ñëåäóþùåé: ìîaeíî ëè â êðèòè÷åñêîì ñëó÷àå ìàëûìè âîçìóùåíèÿìè ïðèâåñòè ìàòðè÷íîå óðàâíåíèå (1) îáùåãî âèäà ê íåêðèòè÷åñêîìó ñëó÷àþ? Ïîñëåäíÿÿ çàäà÷à îòíîñèòñÿ ê çàäà÷àì î ðåãóëÿðèçàöèè [6,14,16,17]. Êàê èçâåñòíî [18], ëþáàÿ (m × n)− ìàòðèöà Q â îïðåäåëåííîì áàçèñå ìîaeåò áûòü ïðåäñòàâëåíà â âèäå…”

Section: îñíîâíîé ðåçóëüòàòunclassified

On the Regularization of a linear matrix equations

2016

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On the Regularization of a Linear Fredholm Boundary-Value Problem by a Degenerate Pulsed Action

Cited by 9 publications

References 8 publications

Boundary value problems for systems of non-degenerate difference-algebraic equations

Boundary value problems for systems of non-degenerate difference-algebraic equations

A сondition for the existence of a unique equilibrium position of the Cauchy problem for linear matrix differential algebraic equations

On the Regularization of a linear matrix equations

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