Periodic solutions of equations with delays depending on time and state
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Date
2023
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Publisher
Faculty of Sciences
Abstract
In this work, two classes of nonlinear functional di⁄erential equations with multiple delays depending on the time and the state are investigated. Using as a main tool a hybrid approach that combines xed point theorems in cones and the Greens functions method, we provide some su¢ cient conditions that guarantee the existence of multiple positive periodic solutions. The main idea consists to dene the Banach space and the cone that facilitate our study on the one hand, and on the other hand they ensure some desired requirements before transforming the problem into an equivalent integral equation whose kernel is a Greensfunction, andhenceapplyingaxedpointtheoreminconeorLeggettWilliams xed point theorem. Keywords: Existence, xedpointtheoremincone, Greensfunction, LeggettWilliams xed point theorem, time and state delay di⁄erential equation