1. Mild solutions for some partial functional integrodifferential equations with finite delay in Fréchet spaces
- Author
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Rachid Bahloul, Sylvain Koumla, and Khalil Ezzinbi
- Subjects
Numerical Analysis ,Pure mathematics ,Work (thermodynamics) ,Control and Optimization ,Applied Mathematics ,Mathematical analysis ,010103 numerical & computational mathematics ,Resolvent formalism ,Function (mathematics) ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Modeling and Simulation ,Resolvent operator ,0101 mathematics ,Mathematics ,Resolvent - Abstract
In this work, we study the existence of mild solutions for some partial functional integrodifferential equations with finite delay in a Frechet spaces. We assume that the linear part has a resolvent operator in the sense given by Grimmer (Trans Am Math Soc 273: 333–349, 1982). The nonlinear part is a sum of a Lipschitzian function and another satisfies the Caratheodory’s conditions. Our approach is based on a nonlinear alternative of Avramescu type and the resolvent operators theory. An application is provided to a reaction-diffusion equation with delay.
- Published
- 2016
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