Averaging in Boundary-Value Problems for Systems of Differential and Integrodifferential Equations

Stanzhitskii, A. N.; Mynbayeva, S. T.; Марчук, Наталія

doi:10.1007/s11253-020-01781-2

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∂X(tx) ∂X1

Introduction1

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2021

2024

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Cited by 5 publications

(2 citation statements)

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“…Let us estimate each term of the sum in (26). Taking into account that ∂X ∂x is Lipschitz and (25), we obtain that the first term in (26) admits the estimate…”

Section: ∂X(tx) ∂Xmentioning

confidence: 99%

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Application of the method of averaging to boundary value problems for differential equations with non-fixed moments of impulse

Stanzhytskyi

Uteshova

Mukash

et al. 2022

Carpathian Math. Publ.

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The method of averaging is applied to study the existence of solutions of boundary value problems for systems of differential equations with non-fixed moments of impulse action. It is shown that if an averaged boundary value problem has a solution, then the original problem is solvable as well. Here the averaged problem for the impulsive system is a simpler problem of ordinary differential equations.

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“…Let us estimate each term of the sum in (26). Taking into account that ∂X ∂x is Lipschitz and (25), we obtain that the first term in (26) admits the estimate…”

Section: ∂X(tx) ∂Xmentioning

confidence: 99%

“…It made it possible to reduce the solution of a boundary value problem for a non-autonomous multifrequency system to the study of a similar problem for an autonomous averaged system. In [24,26], this method was applied to boundary value problems for systems of integro-differential equations.…”

Section: Introductionmentioning

confidence: 99%