Integrodifferential equations on time scales with Henstock-Kurzweil-Pettis delta integrals
type: Item
instance of: scholarly article
title: Integrodifferential equations on time scales with Henstock-Kurzweil-Pettis delta integrals
zbMATH Open document ID: 1205.34135
DOI: 10.1155/2010/836347
author: Aneta Sikorska-Nowak
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/227284
review text: Summary: We prove existence theorems for integro-differential equations \[ x^\Delta(t)=f(t,x(t),\int^t_0k(t,s,x(s))\,\Delta s),\quad x(0)=x_0,\;t\in I_a=[0,a]\cap T,\;a\in\mathbb R_+, \] where \(T\) denotes a time scale (nonempty closed subset of real numbers \(\mathbb R\)), and \(I_a\) 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.
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 26A39
Mathematics Subject Classification ID: 34K30
zbMATH DE Number: 5791637
Wikidata QID: Q58649936
MaRDI profile type: Publication
OpenAlex ID: W1989874262
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description: scientific article; zbMATH DE number 5791637