Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

Aneta Sikorska-Nowak

Journal of Applied Mathematics, 2007, vol. 2007, 1-12

Abstract:

We prove existence theorems for the integrodifferential equation x ' ( t )= f ( t , x ( t ) , ∫ 0 t k ( t , s , x ( s ) ) d s ) , x ( 0 ) = x 0 , t ∈ I a = [ 0 , a ] , a > 0 , where f , k , x are functions with values in a Banach space E and the integral is taken in the sense of HL. Additionally, the functions f and k satisfy certain boundary conditions expressed in terms of the measure of noncompactness.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:031572

DOI: 10.1155/2007/31572

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