Abstract

CARRILLO, Génesis. Existence of bounded solutions for retarded equations with infinite delay, impulses, and nonlocal condition. Novasinergia [online]. 2020, vol.3, n.2, pp.67-79.  Epub Dec 01, 2020. ISSN 2631-2654.

Abstract: In this work, we study the existence of bounded solutions for a semilinear retarded equation with infinite delay, impulse, and non-local conditions. We also show that under some conditions this bounded solution is unique, periodic, or almost periodic depending on the conditions imposed on the terms involving the equation. Through this work, we shall assume that the associated linear equation has an exponential dichotomy, allowing us to find a formula for the bounded solutions, and from this formula, we are able to apply Banach Fixed Point Theorem to prove the existence of such bounded solutions

Keywords : Exponential dichotomy; bounded solution; unique; periodic; almost periodic.

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