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Zbl 1214.34064
Abada, Nadjet; Benchohra, Mouffak; Hammouche, Hadda
Existence results for semilinear differential evolution equations with impulses and delay. (English)
[J] Cubo 12, No. 2, 1-17 (2010). ISSN 0716-7776

The authors 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. They use a fixed point theorem due to Burton and Kirk to prove the existence of mild solutions and Dhage's fixed point theorem for the existence of extremal solutions.
[Daniel Pasca (Oradea)]

MSC 2000:: *34K30 Functional-differential equations in abstract spaces
34K45 Equations with impulses
47N20 Appl. of operator theory to differential and integral equations

Keywords: densely defined operator; impulsive functional differential equations; fixed point; semigroups; mild solutions; extremal mild solutions; nonlocal condition; separable Banach space

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