In this study, we employ the fixed point theorem of Krasnoselskii andthe concepts of separate and large contractions to show the existenceof a periodic solution of a highly nonlinear delay differential equation.Also, we give a classification theorem providing sufficient conditions foran operator to be a large contraction, and hence, a separate contraction.Finally, under slightly different conditions, we obtain the existence ofa positive periodic solution.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, we employ the fixed point theorem of Krasnoselskii andthe concepts of separate and large contractions to show the existenceof a periodic solution of a highly nonlinear delay differential equation.Also, we give a classification theorem providing sufficient conditions foran operator to be a large contraction, and hence, a separate contraction.Finally, under slightly different conditions, we obtain the existence ofa positive periodic solution.
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Key Findings & Data:In this study, we employ the fixed point theorem of Krasnoselskii andthe concepts of separate and large contractions to show the existenceof a periodic solution of a highly nonlinear delay differential equation.Also, we give a classification theorem providing sufficient conditions foran operator to be a large contraction, and hence, a separate contraction.Finally, under slightly different conditions, we obtain the existence ofa positive periodic solution.
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Conclusion & Impact:In this study, we employ the fixed point theorem of Krasnoselskii andthe concepts of separate and large contractions to show the existenceof a periodic solution of a highly nonlinear delay differential equation.Also, we give a classification theorem providing sufficient conditions foran operator to be a large contraction, and hence, a separate contraction.Finally, under slightly different conditions, we obtain the existence ofa 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 andthe concepts of separate and large contractions to show the existenceof a periodic solution of a highly nonlinear delay differential equation.Also, we give a classification theorem providing sufficient conditions foran operator to be a large contraction, and hence, a separate contraction.Finally, under slightly different conditions, we obtain the existence ofa positive periodic solution.
ADIVAR, M., ISLAM, M. N., RAFFOUL, Y. N. (2022). SEPARATE CONTRACTION AND EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR DELAY DIFFERENTIAL EQUATIONS. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 1, 1–13. https://ajindex.com/articles/530462
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