Abstract and Applied Analysis

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

Aneta Sikorska-Nowak

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 836347, 17 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620745

Digital Object Identifier
doi:10.1155/2010/836347

Mathematical Reviews number (MathSciNet)
MR2669088

Zentralblatt MATH identifier
1205.34135

Citation

Sikorska-Nowak, Aneta. Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals. Abstr. Appl. Anal. 2010 (2010), Article ID 836347, 17 pages. doi:10.1155/2010/836347. https://projecteuclid.org/euclid.aaa/1288620745


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