Geodesic
On estimates of solutions of boundary-value problems for implicit differential equations with deviating argument
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 186 (2020), pp. 38-44

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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.
Keywords: implicit differential equation, boundary-value problem, solvability condition, estimate of solution, ordered covering mapping, differential inequality. 
@article{INTO_2020_186_a4,
     author = {T. V. Zhukovskaya and I. D. Serova},
     title = {On estimates of solutions of boundary-value problems for implicit differential equations with deviating argument},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {38--44},
     publisher = {mathdoc},
     volume = {186},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_186_a4/}
}
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T. V. Zhukovskaya; I. D. Serova. On estimates of solutions of boundary-value problems for implicit differential equations with deviating argument. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 186 (2020), pp. 38-44. http://geodesic.mathdoc.fr/item/INTO_2020_186_a4/