Abstract and Applied Analysis

Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions

Carlos Lizama and Juan C. Pozo

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Abstract

Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions u ( t ) = A u ( t ) + 0 t B ( t - s ) u ( s ) d s + f ( t , u ( t ) ) , t [ 0,1 ] , u ( 0 ) = g ( u ) , where A : D ( A ) X X , and for every t [ 0,1 ] the maps B ( t ) : D ( B ( t ) ) X X are linear closed operators defined in a Banach space X . We assume further that D ( A ) D ( B ( t ) ) for every t [ 0,1 ] , and the functions f : [ 0,1 ] × X X and g : C ( [ 0,1 ] ; X ) X are X -valued functions which satisfy appropriate conditions.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 647103, 15 pages.

Dates
First available in Project Euclid: 7 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1399486652

Digital Object Identifier
doi:10.1155/2012/647103

Mathematical Reviews number (MathSciNet)
MR3004930

Zentralblatt MATH identifier
1261.34062

Citation

Lizama, Carlos; Pozo, Juan C. Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 647103, 15 pages. doi:10.1155/2012/647103. https://projecteuclid.org/euclid.aaa/1399486652


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