Differential and Integral Equations

Existence and uniqueness of $\bf C^{1+\alpha}$-strict solutions for integro-differential equations with state-dependent delay

Eduardo Hernández and Jianhong Wu

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Abstract

We study the existence and uniqueness of strict and $\bf C^{1+\alpha}$-strict solutions for a general class of abstract integro-differential equations with state-dependent delay. Some examples concerning partial integro-differential equations with state dependent delay are presented.

Article information

Source
Differential Integral Equations, Volume 32, Number 5/6 (2019), 291-322.

Dates
First available in Project Euclid: 3 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1554256868

Mathematical Reviews number (MathSciNet)
MR3938341

Zentralblatt MATH identifier
07070542

Subjects
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35R10: Partial functional-differential equations 34K40: Neutral equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

Citation

Hernández, Eduardo; Wu, Jianhong. Existence and uniqueness of $\bf C^{1+\alpha}$-strict solutions for integro-differential equations with state-dependent delay. Differential Integral Equations 32 (2019), no. 5/6, 291--322. https://projecteuclid.org/euclid.die/1554256868


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