EXISTENCE AND STABILIZATION FOR IMPULSIVE DIFFERENTIAL EQUATIONS OF SECOND ORDER WITH MULTIPLE DELAYS

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Pinelas S., Tunç O., Korkmaz E., Tunç C.

Electronic Journal of Differential Equations, vol.2024, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2024
  • Publication Date: 2024
  • Doi Number: 10.58997/ejde.2024.07
  • Journal Name: Electronic Journal of Differential Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Keywords: existence of solutions; multiple delays, exponentially stabilization, Impulsive delay differential equations
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

Existence and stability of solutions are important parts in the qualitative study of delay differential equations. The stabilizing by impos-ing proper impulse controls are used in many areas of natural sciences and engineering. This article provides sufficient conditions for the existence and exponential stabilization of solutions to delay impulsive differential equations of second-order with multiple delays. The main tools in this article are the Schaefer fixed point theorem, fixed impulse effects, and Lyapunov-Krasovskii functionals. The outcomes extend earlier results in the literature.