A notion of boundedness for hyperfunctions and Massera type theorems

Yasunori Okada

Banach Center Publications (2012)

  • Volume: 97, Issue: 1, page 101-111
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Yasunori Okada. "A notion of boundedness for hyperfunctions and Massera type theorems." Banach Center Publications 97.1 (2012): 101-111. <http://eudml.org/doc/282137>.

@article{YasunoriOkada2012,
abstract = { 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. },
author = {Yasunori Okada},
journal = {Banach Center Publications},
keywords = {bounded hyperfunctions; Massera type theorems},
language = {eng},
number = {1},
pages = {101-111},
title = {A notion of boundedness for hyperfunctions and Massera type theorems},
url = {http://eudml.org/doc/282137},
volume = {97},
year = {2012},
}

TY - JOUR
AU - Yasunori Okada
TI - A notion of boundedness for hyperfunctions and Massera type theorems
JO - Banach Center Publications
PY - 2012
VL - 97
IS - 1
SP - 101
EP - 111
AB - 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.
LA - eng
KW - bounded hyperfunctions; Massera type theorems
UR - http://eudml.org/doc/282137
ER -

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