Existence of mild solutions of second order evolution integro-differential equations in the Fre'chet spaces

	Existence of mild solutions of second order evolution integro-differential equations in the Fre'chet spaces
Journal of Mathematical Modeling
مقاله 4، دوره 7، شماره 3، آذر 2019، صفحه 305-318 اصل مقاله (275.78 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2019.13018.1256
نویسنده
Adel Jawahdou^*
Department of Mathematics, Bizerte Preparatory Engineering Institute, Tunisia
چکیده
In this article, we shall establish sufficient conditions for the existence of mild solutions for second order semilinear integro-differential evolution equations in Fre'chet spaces $C(\mathbb{R}_+ , E)$, where $E$ is an Banach space. Our approach is based on the concept of a measure of noncompactness and Tykhonoff fixed point theorem. For illustration we give an example.
کلیدواژه‌ها
Semilinear integro-differential equation؛ measure of noncompactness؛ mild solutions؛ evolution system؛ Tykhonoff fixed point theorem

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