Kodai Mathematical Journal

Existence and uniqueness of periodic solutions for parabolic equation with nonlocal delay

Qiang Li, Yongxiang Li, and Pengyu Chen

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Abstract

This paper deals with the existence and uniqueness of time periodic solutions for the general periodic parabolic equation boundary problem with nonlocal delay. We apply operator semigroup theory and monotone iterative technique of lower and upper solutions to obtain the existence and uniqueness of ω-periodic mild solutions of some abstract evolution equation under some quasimonotone conditions. In the end, applying our abstract results to parabolic equation with nonlocal delay, we get the existence and uniqueness of ω-periodic solution, which generalize the recent conclusions on this issue.

Article information

Source
Kodai Math. J., Volume 39, Number 2 (2016), 276-289.

Dates
First available in Project Euclid: 6 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1467830137

Digital Object Identifier
doi:10.2996/kmj/1467830137

Mathematical Reviews number (MathSciNet)
MR3520512

Zentralblatt MATH identifier
06624562

Citation

Li, Qiang; Li, Yongxiang; Chen, Pengyu. Existence and uniqueness of periodic solutions for parabolic equation with nonlocal delay. Kodai Math. J. 39 (2016), no. 2, 276--289. doi:10.2996/kmj/1467830137. https://projecteuclid.org/euclid.kmj/1467830137


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