Journal of Integral Equations and Applications
- J. Integral Equations Applications
- Volume 28, Number 4 (2016), 441-458.
Application of measure of noncompactness to Volterra equations of convolution type
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.
J. Integral Equations Applications, Volume 28, Number 4 (2016), 441-458.
First available in Project Euclid: 15 December 2016
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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. https://projecteuclid.org/euclid.jiea/1481792835