Journal of Integral Equations and Applications

Application of measure of noncompactness to Volterra equations of convolution type

Edgardo Alvarez and Carlos Lizama

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Sufficient conditions for the existence of at least one solution of a nonlinear integral equation with a general kernel are established. The existence result is proved in $C([0,T],E)$, where $E$ denotes an arbitrary Banach space. We use the Darbo-Sadovskii fixed point theorem and techniques of measure of noncompactness. We extend and generalize results obtained by other authors in the context of fractional differential equations. One example illustrates the theoretical results.

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J. Integral Equations Applications, Volume 28, Number 4 (2016), 441-458.

First available in Project Euclid: 15 December 2016

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Primary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 45D05: Volterra integral equations [See also 34A12] 45N05: Abstract integral equations, integral equations in abstract spaces

Volterra equations of convolution type nonlinear functional integral equations Darbo's fixed point theorem measure of noncompactness


Alvarez, Edgardo; Lizama, Carlos. Application of measure of noncompactness to Volterra equations of convolution type. J. Integral Equations Applications 28 (2016), no. 4, 441--458. doi:10.1216/JIE-2016-28-4-441.

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