Integrodifferential Equations on Time Scales with Henstock‐Kurzweil‐Pettis Delta Integrals

Aneta Sikorska-Nowak

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: We prove existence theorems for integro‐differential equations xΔ(t)=f(t,x(t),∫0tk(t,s,x(s))Δs), x(0) = x0, t ∈ Ia = [0, a]∩T, a ∈ R+, where T denotes a time scale (nonempty closed subset of real numbers R), and Ia is a time scale interval. The functions f, k are weakly‐weakly sequentially continuous with values in a Banach space E, and the integral is taken in the sense of Henstock‐Kurzweil‐Pettis delta integral. This integral generalizes the Henstock‐Kurzweil delta integral and the Pettis integral. Additionally, the functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of weak noncompactness. Moreover, we prove Ambrosetti′s lemma.

Date: 2010
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https://doi.org/10.1155/2010/836347

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:836347

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