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2016 Volterra integral equations on variable exponent Lebesgue spaces
R.E. Castillo, J.C. Ramos-Fernández, E.M. Rojas
J. Integral Equations Applications 28(1): 1-29 (2016). DOI: 10.1216/JIE-2016-28-1-1

Abstract

In this paper, in the framework of Lebesgue spaces with variable exponent, we are going to provide conditions for the existence and uniqueness of the solutions of a class of Volterra integral equations induced by Carath\'eodory functions having diverse growth behaviors. To attain our goals, we will use topological degree theory for condensing maps and fixed point results for the sum of mappings of contractive type.

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R.E. Castillo. J.C. Ramos-Fernández. E.M. Rojas. "Volterra integral equations on variable exponent Lebesgue spaces." J. Integral Equations Applications 28 (1) 1 - 29, 2016. https://doi.org/10.1216/JIE-2016-28-1-1

Information

Published: 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1334.45003
MathSciNet: MR3488153
Digital Object Identifier: 10.1216/JIE-2016-28-1-1

Subjects:
Primary: 45D05 , 46E30 , 47B38 , 47H10

Keywords: contractive mapping , Variable Lebesgue space , Volterra integral equation

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.28 • No. 1 • 2016
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