Necessary and Sufficient Conditions for Oscillation of Second-Order Delay Differential Equations

Shyam Sundar Santra

doi:10.2478/tmmp-2020-0009

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Necessary and Sufficient Conditions for Oscillation of Second-Order Delay Differential Equations

Tatra Mountains Mathematical Publications

Volume 75 (2020): Issue 1 (April 2020)

By: Shyam Sundar Santra

Open Access

|Apr 2020

Abstract

In this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form ${(r {(x^{'})}^{γ})}^{'} (t) + q (t) x^{α} (τ (t)) = 0$ {\left( {r{{\left( {x'} \right)}^\gamma }} \right)^\prime }\left( t \right) + q\left( t \right){x^\alpha }\left( {\tau \left( t \right)} \right) = 0

Under the assumption ∫^∞(r(n))^−1/γdη=∞, we consider the two cases when γ > α and γ < α. Further, some illustrative examples showing applicability of the new results are included, and state an open problem.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2020-0009 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 135 - 146

Submitted on: Mar 30, 2019

Published on: Apr 24, 2020

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

oscillation,

non-oscillation,

delay,

linear,

Lebesgue’s dominated convergence theorem

Related subjects:

Mathematics,

General mathematics

© 2020 Shyam Sundar Santra, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 75 (2020): Issue 1 (April 2020)