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This article is cited in 1 scientific paper (total in 1 paper)
On one class of systems of differential equations with periodic coefficients in linear terms
G. V. Demidenko Sobolev Institute of Mathematics, Novosibirsk, Russia
Abstract:
Under consideration is some class of systems of nonlinear differential equations. The exponentially dichotomous linear part of the systems is assumed to have periodic coefficients. Using the author's criterion of exponential dichotomy, we establish the conditions of existence of periodic solutions and prove stability of the solutions under small perturbations of coefficients in the linear part and nonlinear terms.
Keywords:
periodic solution, exponential dichotomy, projection, Lyapunov differential equation, Green matrix, Sobolev space.
Received: 01.06.2021 Revised: 31.07.2021 Accepted: 11.08.2021
Citation:
G. V. Demidenko, “On one class of systems of differential equations with periodic coefficients in linear terms”, Sibirsk. Mat. Zh., 62:5 (2021), 995–1012; Siberian Math. J., 62:5 (2021), 805–821
Linking options:
https://www.mathnet.ru/eng/smj7610 https://www.mathnet.ru/eng/smj/v62/i5/p995
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Abstract page: | 182 | Full-text PDF : | 63 | References: | 28 | First page: | 5 |
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