Abstract:
A two-point boundary-value problem for an implicit differential equation with a deviating argument is examined. An existence theorem and an estimate for the solution are obtained, which is similar to the Chaplygin theorem on differential inequalities. We use results on equations with covering and monotonic mappings in partially ordered spaces and conditions for ordered covering of the Nemytskii operator in the space of measurable essentially bounded functions.
Citation:
T. V. Zhukovskaya, I. D. Serova, “On estimates of solutions of boundary-value problems for implicit differential equations with deviating argument”, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 186, VINITI, Moscow, 2020, 38–44
\Bibitem{ZhuSer20}
\by T.~V.~Zhukovskaya, I.~D.~Serova
\paper On estimates of solutions of boundary-value problems for implicit differential equations with deviating argument
\inbook Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 186
\pages 38--44
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into710}
\crossref{https://doi.org/10.36535/0233-6723-2020-186-38-44}
Linking options:
https://www.mathnet.ru/eng/into710
https://www.mathnet.ru/eng/into/v186/p38
This publication is cited in the following 3 articles:
Jervin Zen Lobo, Sanket Tikare, Mahammad Khuddush, “Chaplygin's method for second-order neutral differential equations with piecewise constant deviating arguments”, J Anal, 2023
S. Benarab, “Dvustoronnie otsenki reshenii kraevykh zadach dlya neyavnykh differentsialnykh uravnenii”, Vestnik rossiiskikh universitetov. Matematika, 26:134 (2021), 216–220
S. Benarab, “O teoreme Chaplygina dlya neyavnogo differentsialnogo uravneniya n-go poryadka”, Vestnik rossiiskikh universitetov. Matematika, 26:135 (2021), 225–233
Citation in format AMSBIB
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