Journal of Integral Equations and Applications

Abstract Volterra equations with state-dependent delay

Carlos Lizama and M. Pilar Velasco

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Abstract

By using the theory of resolvent families, fixed point theorems and measures of noncompactness, we prove the existence of mild solutions on a compact interval for a semilinear Volterra equation with state-dependent delay. An example is given.

Article information

Source
J. Integral Equations Applications, Volume 27, Number 2 (2015), 219-231.

Dates
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1441790287

Digital Object Identifier
doi:10.1216/JIE-2015-27-2-219

Mathematical Reviews number (MathSciNet)
MR3395969

Zentralblatt MATH identifier
1328.34075

Subjects
Primary: 26A33: Fractional derivatives and integrals 34A08: Fractional differential equations 34K37: Functional-differential equations with fractional derivatives 45G05: Singular nonlinear integral equations 45J05: Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]

Keywords
Volterra Equations resolvent family mild solution fixed point state-dependent delay measure of noncompactness Banach spaces

Citation

Lizama, Carlos; Velasco, M. Pilar. Abstract Volterra equations with state-dependent delay. J. Integral Equations Applications 27 (2015), no. 2, 219--231. doi:10.1216/JIE-2015-27-2-219. https://projecteuclid.org/euclid.jiea/1441790287


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