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Necessary and sufficient conditions for oscillation of nonlinear first-order forced differential equations with several delays of neutral type

  • Sandra Pinelas ORCID logo EMAIL logo and Shyam S. Santra
Published/Copyright: September 24, 2019

Abstract

In this work, necessary and sufficient conditions are obtained such that every solution of nonlinear neutral first-order differential equations with several delays of the form

(x(t)+r(t)x(t-τ))+i=1mϕi(t)H(x(t-σi))=f(t)

is oscillatory or tends to zero as t. This problem is considered in various ranges of the neutral coefficient r. Finally, some illustrating examples are presented to show that feasibility and effectiveness of main results.

MSC 2010: 34C10; 34C15

Funding statement: This work is supported by the Department of Science and Technology (DST), New Delhi, India, through the bank instruction order No. DST/INSPIRE Fellowship/2014/140, dated Sept. 15, 2014. The publication was supported by the Ministry of Education and Science of the Russian Federation (Agreement No. 02.a03.21.0008).

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Received: 2018-02-07
Revised: 2019-02-04
Accepted: 2019-09-04
Published Online: 2019-09-24
Published in Print: 2019-10-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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