Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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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)
  • Received : 2017.11.08
  • Accepted : 2018.12.11
  • Published : 2019.03.23
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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

Acknowledgement

Supported by : Department of Science and Technology (DST), British Council

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