A NEW OSCILLATION RESULT FOR NONLINEAR DIFFERENTIAL EQUATIONS WITH NONMONOTONE DELAY

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Kilic N., ÖCALAN Ö.

Miskolc Mathematical Notes, vol.24, no.2, pp.841-851, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.18514/mmn.2023.4015
  • Journal Name: Miskolc Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.841-851
  • Keywords: nonlinear delay equation, nonmonotone argument, oscillatory solution
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

In this article, our objective is to study the oscillation of first order nonlinear delay differential equation (Formula Presented) where the functions p(t) and τ(t) are functions of nonnegative real numbers, τ(t) is not necessarily monotone such that τ(t) ≤ t for t ≥ t0, (Formula Presented) and xf(x) > 0 for x ≠ 0. Also, we establish a new oscillation condition involving both limsup and liminf. Finally, we present two examples to demonstrate the main result.