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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.2 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000200001 

CUBO A Mathematical Journal Vol.12, N°02, (1-17). June 2010

 

Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay

 

Nadjet Abada, Mouffak Benchohra 1 and Hadda Hammouche

Département de Mathématiques, Université Mentouri Constantine,Francia email: n65abada@yahoo.fr

Laboratoire de Mathématiques, Université de Sidi Bel Abbés, BP 89, 22000 Sidi Bel Abbés, Algérie. email: benchohra@univ-sba.dz

Département de Mathematiques, Université Kasdi Merbah Ouargla, Algérie. email: h.hammouche@yahoo.fr


ABSTRACT

In this paper, we establish sufficient conditions for the existence of mild and extremal solutions for some densely defined impulsive functional differential equations in separable Banach spaces with local and nonlocal conditions. We shall rely for the existence of mild solutions on a fixed point theorem due to Burton and Kirk for the sum of completely continuous and contraction operators, and for the existence of extremal solutions on Dhage’s fixed point theorem.

Key words and phrases: Densely defined operator, impulsive functional differential equations, fixed point, semigroups, mild solutions, extremal mild solutions, nonlocal condition, separable Banach space.


RESUMEN

En este artículo establecemos condiciones suficientes para la existencia de soluciones suaves y extremas para algunas ecuaciones diferenciales funcionales impulsivas densamente definidas en espacios de Banach separables con condiciones locales y no locales. Para la existencia de soluciones suaves usaremos un teorema de punto fijo debido a Burton y Kirk para la suma de un operador completamente continuo y otro contractivo; para la existencia de soluciones extremas usaremos el teorema de punto fijo de Dhage.

AMS (MOS) Subj. Class.: 34A37, 34K30, 34K35, 34K45.


Notas

1Corresponding author

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Received: December 2008.

Revised: January 2009.