IJPAM: Volume 113, No. 1 (2017)

Title

OSCILLATION OF SUBLINEAR AND SUPERLINEAR
SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS

Authors

A.K. Tripathy$^1$, A.K. Sethi$^2$
$^{1,2}$Department of Mathematics
Sambalpur University
Sambalpur, 768019, INDIA

Abstract

In this work, we establish the necessary and sufficient conditions for oscillation of a class of functional differential equations of the form:

\begin{eqnarray*} (r(t)(x(t)+p(t)x(\tau(t)))')'+q(t)G(x(\sigma(t)))+v(t)H(x(\eta(t)))=0 \end{eqnarray*}


under the assumption that

\begin{eqnarray*} \int_{0}^{\infty}\frac{dt}{r(t)}&=&\infty \end{eqnarray*}


for various ranges of $p(t)$.

History

Received: November 2, 2016
Revised: February 22, 2017
Published: February 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 34K, 34C10
Key Words and Phrases: oscillation, nonoscillation, neutral, delay, nonlinear

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How to Cite?

DOI: 10.12732/ijpam.v113i1.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 1
Pages: 73 - 91


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