Differential and Integral Equations

Existence and stability in the $\alpha$-norm for some partial functional differential equations with infinite delay

Rachid Benkhalti and Khalil Ezzinbi

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Abstract

In this work, we discuss the existence, regularity and stability of solutions for some partial functional differential equations with infinite delay. We assume that the linear part generates an analytic semigroup on a Banach space $X$ and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.

Article information

Source
Differential Integral Equations, Volume 19, Number 5 (2006), 545-572.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050442

Mathematical Reviews number (MathSciNet)
MR2235141

Zentralblatt MATH identifier
1212.34237

Subjects
Primary: 34K06: Linear functional-differential equations
Secondary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 34K20: Stability theory 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N20: Applications to differential and integral equations

Citation

Benkhalti, Rachid; Ezzinbi, Khalil. Existence and stability in the $\alpha$-norm for some partial functional differential equations with infinite delay. Differential Integral Equations 19 (2006), no. 5, 545--572. https://projecteuclid.org/euclid.die/1356050442


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