Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces

Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces

In this paper we consider the semilinear differential equation with deviated argument in a Fréchet space $x^{\prime}(t) = A x(t) + f(t, x(t), x[\alpha(x(t),t)]),$ $t \in {\mathbb{R}}$, where $A$ is the infinitesimal (bounded) generator of a $C_{0}$-semigroup satisfying some conditions of exponential...

Full description

Bibliographic Details
Main Author: C. Gal
Format: Article
Language:English
Published: University of Szeged 2006-10-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=255
id doaj-690127763f4d44e98dd81d7f59b4aebf
record_format Article
spelling doaj-690127763f4d44e98dd81d7f59b4aebf2021-07-14T07:21:19ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752006-10-012006161810.14232/ejqtde.2006.1.16255Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spacesC. Gal0Morgan State University, Baltimore, MD, U.S.A.In this paper we consider the semilinear differential equation with deviated argument in a Fréchet space $x^{\prime}(t) = A x(t) + f(t, x(t), x[\alpha(x(t),t)]),$ $t \in {\mathbb{R}}$, where $A$ is the infinitesimal (bounded) generator of a $C_{0}$-semigroup satisfying some conditions of exponential stability. Under suitable conditions on the functions $f$ and $\alpha$ we prove the existence and uniqueness of an almost automorphic mild solution to the equation.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=255
collection DOAJ
language English
format Article
sources DOAJ
author C. Gal
spellingShingle C. Gal
Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
Electronic Journal of Qualitative Theory of Differential Equations
author_facet C. Gal
author_sort C. Gal
title Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
title_short Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
title_full Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
title_fullStr Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
title_full_unstemmed Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
title_sort almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in fréchet spaces
publisher University of Szeged
series Electronic Journal of Qualitative Theory of Differential Equations
issn 1417-3875
1417-3875
publishDate 2006-10-01
description In this paper we consider the semilinear differential equation with deviated argument in a Fréchet space $x^{\prime}(t) = A x(t) + f(t, x(t), x[\alpha(x(t),t)]),$ $t \in {\mathbb{R}}$, where $A$ is the infinitesimal (bounded) generator of a $C_{0}$-semigroup satisfying some conditions of exponential stability. Under suitable conditions on the functions $f$ and $\alpha$ we prove the existence and uniqueness of an almost automorphic mild solution to the equation.
url http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=255
work_keys_str_mv AT cgal almostautomorphicmildsolutionstosomesemilinearabstractdifferentialequationswithdeviatedargumentinfrechetspaces
_version_ 1721303832623841280

Similar Items