Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 708–711 | Cite as

On a Certain First-Order Differential Equation with Delay

  • A. S. Larionov


We consider the Cauchy problem for a first-order quasilinear differential equation with delayed argument of neutral type, and obtain sufficient conditions of 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 and phrases

differential equation delay  monotonic operator problem Cauchy solvability 

AMS Subject Classification

34K10 34K40 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Bratsk State UniversityBratskRussia

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