Baker, F., El-Morshedy, H. (2015). On the distribution of zeros of solutions of a first order neutral differential equation. test, 4(1), 1-9. doi: 10.21608/sjdfs.2015.194323
F. A. Baker; H. A. El-Morshedy. "On the distribution of zeros of solutions of a first order neutral differential equation". test, 4, 1, 2015, 1-9. doi: 10.21608/sjdfs.2015.194323
Baker, F., El-Morshedy, H. (2015). 'On the distribution of zeros of solutions of a first order neutral differential equation', test, 4(1), pp. 1-9. doi: 10.21608/sjdfs.2015.194323
Baker, F., El-Morshedy, H. On the distribution of zeros of solutions of a first order neutral differential equation. test, 2015; 4(1): 1-9. doi: 10.21608/sjdfs.2015.194323

On the distribution of zeros of solutions of a first order neutral differential equation

Scientific Journal for Damietta Faculty of Science
Article 1, Volume 4, Issue 1, 2015, Pages 1-9    PDF (3.63 M)
Document Type: Original articles
DOI: 10.21608/sjdfs.2015.194323
Authors
F. A. Baker; H. A. El-Morshedy*
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
Abstract
This paper is devoted to study the distribution of zeros of all solutions of the first-order neutral
differential equation
[x(t) — px(t — T)]' + Q(t)x(t — σ) = 0, t > t0,
where p > 1, τ,σ > 0 , and Q ∈ C([t0, ∞), (0, ∞)).
We obtain new estimates for the distance between adjacent zeros of all solutions of the above equation
under suitable criteria. Our results are supported with illustrative examples.
Keywords
Distribution of zeros; Oscillation, Neutral differential equations
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