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2010 Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals
Aneta Sikorska-Nowak
Abstr. Appl. Anal. 2010: 1-17 (2010). DOI: 10.1155/2010/836347

Abstract

We prove existence theorems for integro-differential equations x Δ ( t ) = f ( t , x ( t ) , 0 t k ( t , s , x ( s ) ) Δ s ) , x ( 0 ) = x 0 , t I a = [ 0 , a ] T , a R + , where T denotes a time scale (nonempty closed subset of real numbers 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.

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Aneta Sikorska-Nowak. "Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals." Abstr. Appl. Anal. 2010 1 - 17, 2010. https://doi.org/10.1155/2010/836347

Information

Published: 2010
First available in Project Euclid: 1 November 2010

zbMATH: 1205.34135
MathSciNet: MR2669088
Digital Object Identifier: 10.1155/2010/836347

Rights: Copyright © 2010 Hindawi

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