International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 339-346

A parabolic differential equation with unbounded piecewise constant delay

Joseph Wiener1 and Lokenath Debnath2

1Department of Mathematics, The University of Texas-Pan American, Edinburg 78539, Texas, USA
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA

Received 26 February 1991; Revised 1 May 1991

Copyright © 1992 Joseph Wiener and Lokenath Debnath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A partial differential equation with the argument [λt] is studied, where [] denotes the greatest integer function. The infinite delay t[λt] leads to difference equations of unbounded order.