Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay





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.


Densely defined operator , impulsive functional differential equations , fixed point , semigroups , mild solutions , extremal mild solutions , nonlocal condition , separable Banach space
  • Nadjet Abada Département de Mathématiques, Université Mentouri Constantine, Constantine, Algéria.
  • Mouffak Benchohra Laboratoire de Mathématiques, Université de Sidi Bel Abbès, BP 89, 22000 Sidi Bel Abbès, Algérie.
  • Hadda Hammouche Département de Mathematiques, Université Kasdi Merbah Ouargla, Algérie.
  • Pages: 1–17
  • Date Published: 2010-06-01
  • Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal

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How to Cite

N. Abada, M. Benchohra, and H. Hammouche, “Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay”, CUBO, vol. 12, no. 2, pp. 1–17, Jun. 2010.