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Zbl 1235.34204
Yan, Zuomao
Existence for a nonlinear impulsive functional integrodifferential equation with nonlocal conditions in Banach spaces. (English)
[J] J. Appl. Math. Inform. 29, No. 3-4, 681-696 (2011). ISSN 1598-5857

Summary: We consider the existence of mild solutions for a certain class of nonlinear impulsive functional evolution integrodifferential equation with nonlocal conditions in Banach spaces. A sufficient condition is established by using Schaefer's fixed point theorem combined with an evolution system. An example is also given to illustrate our result.

MSC 2000:: *34K30 Functional-differential equations in abstract spaces
34K45 Equations with impulses
34K10 Boundary value problems for functional-differential equations
47N20 Appl. of operator theory to differential and integral equations

Keywords: nonlinear impulsive functional integro differential equations; fixed point; linear evolution system; nonlocal conditions

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Zentralblatt MATH Berlin [Germany]