Bulletin of the Belgian Mathematical Society - Simon Stevin

Solutions to abstract integral equations and infinite delay evolution equations

Jin Liang and Ti-Jun Xiao

Full-text: Open access

Abstract

We establish new and general existence theorems of Lipschitz continuous solutions to integral equations with infinite delay in Banach spaces, as well as of strong and classical solutions to the Cauchy problem for some evolution equations with infinite delay. An example is given to illustrate the abstract result.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 5 (2011), 793-804.

Dates
First available in Project Euclid: 13 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1323787167

Digital Object Identifier
doi:10.36045/bbms/1323787167

Mathematical Reviews number (MathSciNet)
MR2918646

Zentralblatt MATH identifier
1236.45009

Subjects
Primary: 45D05: Volterra integral equations [See also 34A12]
Secondary: 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

Keywords
Lipschitz continuity existence Cauchy problem abstract integral equation infinite delay evolution equation

Citation

Liang, Jin; Xiao, Ti-Jun. Solutions to abstract integral equations and infinite delay evolution equations. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 5, 793--804. doi:10.36045/bbms/1323787167. https://projecteuclid.org/euclid.bbms/1323787167


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