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

Aneta Sikorska-Nowak

Journal of Applied Mathematics, 2007, vol. 2007, issue 1

Abstract: We prove existence theorems for the integrodifferential equation x′(t)=f(t,x(t),∫0tk(t,s, x(s))ds), x(0) = x0, t ∈ Ia = [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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https://doi.org/10.1155/2007/31572

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2007:y:2007:i:1:n:031572

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