Geodesic
On a certain first-order differential equation with delay
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 61-63.

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We consider the Cauchy problem for a first-order quasilinear differential equation with delayed argument of neutral type, and obtain sufficient conditions of the existence and uniqueness of its solutions. Proofs of the solvability of nonlinear problems, estimates of solutions, and constructions of approximate methods are based on Chaplygin-type theorems on differential inequalities.
Keywords: differential equation, delay , monotonic operator, problem Cauchy, solvability. 
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     author = {A. S. Larionov},
     title = {On a certain first-order differential equation with delay},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {61--63},
     publisher = {mathdoc},
     volume = {132},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_132_a13/}
}
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A. S. Larionov. On a certain first-order differential equation with delay. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Tome 132 (2017), pp. 61-63. http://geodesic.mathdoc.fr/item/INTO_2017_132_a13/