For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains. In this article, after recalling the terminology, we briefly review our approach to the equations with finite delay, and announce our recent result on some classes of equations with infinite delay.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-7,
author = {Yasunori Okada},
title = {A notion of boundedness for hyperfunctions and Massera type theorems},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {101-111},
zbl = {1262.32007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-7}
}
Yasunori Okada. A notion of boundedness for hyperfunctions and Massera type theorems. Banach Center Publications, Tome 97 (2012) pp. 101-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-7/