International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 6, Pages 347-356
doi:10.1155/S0161171201006561
Modified Wiener equations
Department of Mathematics, University of Texas, Pan American, Edinburg 78539, TX, USA
Received 16 January 2001
To the memory of the late Prof Joseph Wiener
Copyright © 2001 Will Watkins. 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.
Abstract
This paper is concerned with a class of functional differential
equations whose argument transforms are involutions. In contrast
to the earlier works in this area, which have used only
involutions with a fixed point, we also admit involutions without
a fixed point. In the first case, an initial value problem for a
differential equation with involution is reduced to an initial
value problem for a higher order ordinary differential equation.
In our case, either two initial conditions or two boundary
conditions are necessary for a solution; the equation is then
reduced to a boundary value problem for a higher order ODE.