Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $ \dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$

Slyusarchuk, V. Yu.

doi:10.1070/sm8684

Sb. Math.

2017

DOI: 10.1070/sm8684

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Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $ \dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$

V. Yu. Slyusarchuk¹

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2020

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On the Reversibility of Nonlinear Autonomous Differential Operators

Slyusarchuk¹

2020

BMJ

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Çãiäíî ç òåîðåìîþ Áàíàõà ïðî îáåðíåíèé îïåðàòîð äëÿ íåïåðåðâíî¨îáîðîòíîñòi ëiíiéíîãî íåïåðåðâíîãî îïåðàòîðà, ùî äi¹ ç îäíîãî áàíàõîâîãî ïðîñòîðó â iíøèé, íåîáõiäíî i äîñòàòíüî, ùîá öåé îïåðàòîð áóâ ñþð'¹êòèâíèì òà ií'¹êòèâíèì. Öèõ âèìîã íàâiòü ó âèïàäêó íåëiíiéíèõ îïåðàòîðiâ äîñòàòíüî äëÿ îáîðîòíîñòi âiäïîâiäíèõ îïåðàòîðiâ. Îäíàê, îáåðíåíi îïåðàòîðè ìîaeóòü íå áóòè íåïåðåðâíèìè. Öå ñòîñó¹òüñÿ äèôåðåíöiéîâíèõ âiäîáðàaeåíü, äëÿ ÿêèõ îáåðíåíi âiäîáðàaeåííÿ ìîaeóòü íå áóòè äèôåðåíöiéîâíèìè. Òîìó äëÿ îáîðîòíîñòi íåëiíiéíèõ îïåðàòîðiâ ïîòðiáíå âèêîíàííÿ äîäàòêîâèõ âèìîã. Äëÿ äèôåðåöiéîâíîãî âiäîáðàaeåííÿ òàêîþ âèìîãîþ ¹ âèêîíàííÿ óìîâè íåâèðîäaeåíîñòi ïîõiäíî¨Ôðåøå âiäîáðàaeåííÿ â êîaeíié òî÷öi ïðîñòîðó, â ÿêîìó äi¹ öå âiäîáðàaeåííÿ. Ó ñòàòòi ðîçãëÿíóòî íåëiíiéíi àâòîíîìíi äèôåðåíöiàëüíi îïåðàòîðè êëàñó C 1 , ùî äiþòü iç ïðîñòîðó îáìåaeåíèõ i íåïåðåðâíî äèôåðåíöiéîâíèõ íà îñi ôóíêöié ó ïðîñòið îáìåaeåíèõ i íåïåðåðâíèõ íà îñi ôóíêöié çi çíà÷åííÿìè â íåñêií÷åííîâèìiðíîìó áàíàõîâîìó ïðîñòîði. Äëÿ òàêèõ îïåðàòîðiâ íàâåäåíî íåîáõiäíi òà äîñòàòíi óìîâè, ïðè âèêîíàííi ÿêèõ öi îïåðàòîðè ¹ äèôåîìîðôiçìàìè êëàñó C 1. Òàêîae íàâåäåíî óìîâè ií'¹êòèâíîñòi òà ñþð'¹êòèâíîñòi äîñëiäaeóâàíèõ îïåðàòîðiâ. Êëþ÷îâi ñëîâà i ôðàçè: óìîâè îáîðîòíîñòi äèôåðåíöiéîâíèõ âiäîáðàaeåíü, óìîâè îáîðîòíîñòi íåëiíiéíèõ àâòîíîìíèõ äèôåðåíöiàëüíèõ îïåðàòîðiâ, óìîâè ií'¹êòèâíîñòi òà ñþð'¹êòèâíîñòi îïåðàòîðiâ.

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On the Reversibility of Nonlinear Autonomous Differential Operators

Slyusarchuk¹

2020

BMJ

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Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $ \dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$

Cited by 1 publication

References 21 publications

On the Reversibility of Nonlinear Autonomous Differential Operators

On the Reversibility of Nonlinear Autonomous Differential Operators

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