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Existence results for semilinear differential evolution equations with impulses and delay. (English) Zbl 1214.34064
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.
MSC:
34K30Functional-differential equations in abstract spaces
34K45Functional-differential equations with impulses
47N20Applications of operator theory to differential and integral equations