Abstract
In this work, we establish sufficient conditions for the existence of solutions for some functional integrodifferential equations with state-dependent delay in Banach spaces. We use \(C_{0}\)-semigroup theory and a fixed point approach based on Banach and Sadovskii’s fixed point theorems, nonlinear alternative for condensing maps, Bihari’s inequality and the technique of equivalent norms. Applications ares provided to a reaction-diffusion equation with state-dependent delay.
Authors
Sylvain Koumla
Département de Mathématiques, Faculté des Sciences et Techniques, Université Adam Barka d’Abéché, Abéché, Chad
Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Ngarkodje Ngarasta
Département de Mathématiques, Faculté des Sciences Exactes et Appliquées, Université de N’Djaména, N’Djaména, Chad
Keywords
Mild solution; Functional integrodifferential equation with state-dependent delay; C₀-semigroup semigroup; Nonlinear alternative; Condensing map
Paper coordinates
S. Koumla, R. Precup, N. Ngarasta, Existence results for some functional integrodifferential equations with state-dependent delay, Differ. Eq. Dyn. Syst., (2023). https://doi.org/10.1007/s12591-023-00661-y
About this paper
Journal
Differential Equations and Dynamical Systems
Publisher Name
Springer International Publishing AG
Print ISSN
09713514
Online ISSN
09746870
google scholar link
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