Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay

• Nadjet Abada ^[1] ; Mouffak Benchohra ^[2] ; Hadda Hammouche ^[3]
  1. [1] Université Mentouri Constantine Département de Mathématiques
  2. [2] Université de Sidi Bel Abbés Laboratoire de Mathématiques
  3. [3] Université Kasdi Merbah Ouargla Département de Mathematiques

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• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 2, 2010, págs. 1-17
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000200001
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• Resumen
  • español

    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.

  • English

    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.

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