SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 41 Issue: 1

SEPARATE CONTRACTION AND EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Murat Adıvar
Muhammad N. Islam
Youssef N. Raffoul
Pages
—
Publication Date
2012-01-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, under slightly different conditions, we obtain the existence of a positive periodic solution.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we employ the fixed point theorem of Krasnoselskii and the concepts of separate and large contractions to show the existence of a periodic solution of a highly nonlinear delay differential equation.
📊
Key Findings & Data:Also, we give a classification theorem providing sufficient conditions for an operator to be a large contraction, and hence, a separate contraction.
💡
Conclusion & Impact:Finally, under slightly different conditions, we obtain the existence of a positive periodic solution.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Krasnoselskii’s fixed point theorem · Large contraction · Periodic solution

Abstract

In this study, we employ the fixed point theorem of Krasnoselskii and the concepts of separate and large contractions to show the existence of a periodic solution of a highly nonlinear delay differential equation. Also, we give a classification theorem providing sufficient conditions for an operator to be a large contraction, and hence, a separate contraction. Finally, under slightly different conditions, we obtain the existence of a positive periodic solution.

🔖

Cite This Article

Adıvar, M., Islam, M. N., Raffoul, Y. N. (2012). SEPARATE CONTRACTION AND EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR DELAY DIFFERENTIAL EQUATIONS. Hacettepe Journal of Mathematics and Statistics, Volume: 41 Issue: 1. https://ajindex.com/articles/1403570

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (8)

  1. Burton, T. A. Stability by Fixed Point Theory for Functional Differential Equations (Dover, New York, 2006).
  2. Kaufmann, E. R. and Raffoul, Y. N. Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale, Electron. J. Differential Equations No. 27, 12pp, 2007.
  3. Kaufmann, E. R. and Raffoul, Y. N. Periodic solutions for a neutral nonlinear dynamical equation on a time scale, J. Math. Anal. Appl. 319 (1), 315–325, 2006.
  4. Liu, Y. and Li, Z. Schaefer type theorem and periodic solutions of evolution equations, J. Math. Anal. Appl. 316, 237–255, 2006.
  5. Liu, Y. and Li, Z. Krasnoselskii type fixed point theorems and applications, Proc. Amer. Math. Soc. 136 (4), 1213–1220, 2008.
  6. Raffoul, Y. N. Periodic solutions for neutral nonlinear differential equations with functional delay, Electron. J. Differential Equations 102, 1–7, 2003.
  7. Raffoul, Y. N. Positive periodic solutions in neutral nonlinear differential equations, E. J. Qualitative Theory of Diff. Equ. 16, 1–10, 2007.
  8. Smart, D. R. Fixed Points Theorems (Cambridge Univ. Press, Cambridge, 1980).