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2019 Solvability and uniform local attractivity for a Volterra equation of convolution type
Luciano Abadias, Edgardo Alvarez, Józef Banaś, Carlos Lizama
J. Integral Equations Applications 31(2): 149-164 (2019). DOI: 10.1216/JIE-2019-31-2-149

Abstract

We show the existence of uniformly locally attractive solutions for a nonlinear Volterra integral equation of convolution type with a general kernel. We use methods and techniques of fixed point theorems and properties of measure of noncompactness. We extend earlier results obtained in the context of integral equations of fractional order. We give new insights about a new and striking relation between the size of data and the fractional order $\alpha >0$ of the kernel $k(t)=t^{\alpha -1}/\Gamma (\alpha )$.

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Luciano Abadias. Edgardo Alvarez. Józef Banaś. Carlos Lizama. "Solvability and uniform local attractivity for a Volterra equation of convolution type." J. Integral Equations Applications 31 (2) 149 - 164, 2019. https://doi.org/10.1216/JIE-2019-31-2-149

Information

Published: 2019
First available in Project Euclid: 23 September 2019

zbMATH: 07118799
MathSciNet: MR4010582
Digital Object Identifier: 10.1216/JIE-2019-31-2-149

Subjects:
Primary: 45D05
Secondary: 34A08, 47H08

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.31 • No. 2 • 2019
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