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http://dx.doi.org/10.5666/KMJ.2019.59.1.73

Necessary and Sufficient Condition for the Solutions of First-Order Neutral Differential Equations to be Oscillatory or Tend to Zero  

Santra, Shyam Sundar (Department of Mathematics, Sambalpur University, Centre for Systems, Dynamics and Control, College of Engineering, Mathematics and Physical Sciences)
Publication Information
Kyungpook Mathematical Journal / v.59, no.1, 2019 , pp. 73-82 More about this Journal
Abstract
In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.
Keywords
Oscillation; nonoscillation; non-linear; delay; neutral differential equations; Knaster-Tarski fixed point theorem and Banach's fixed point theorem;
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