A notion of boundedness for hyperfunctions and Massera type theorems
Volume 97 / 2012
Banach Center Publications 97 (2012), 101-111
MSC: Primary 32A45; Secondary 34K13.
DOI: 10.4064/bc97-0-7
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.
