Electron. J. Diff. Equ.,
Vol. 2011(2011), No. 02, pp. 113.
Initialvalue problems for firstorder differential recurrence
equations with autoconvolution
Mircea Cirnu
Abstract:
A differential recurrence equation consists of a sequence of
differential equations, from which must be determined by
recurrence a sequence of unknown functions. In this article, we
solve two initialvalue problems for some new types of nonlinear
(quadratic) first order homogeneous differential recurrence
equations, namely with discrete autoconvolution and with
combinatorial autoconvolution of the unknown functions. In
both problems, all initial values form a geometric progression,
but in the second problem the first initial value is exempted
and has a prescribed form.
Some preliminary results showing the importance of the
initial conditions are obtained by reducing the differential
recurrence equations to algebraic type.
Final results about solving the considered initial
value problems, are shown by mathematical induction. However,
they can also be shown by changing the unknown
functions, or by the generating function method.
So in a remark, we give a proof of the first theorem by the
generating function method.
Submitted September 10, 2010. Published January 4, 2011.
Math Subject Classifications: 11B37, 34A12.
Key Words: Differential recurrence equations; discrete autoconvolution;
algebraic recurrence equations.
Show me the PDF file (230 KB),
TEX file, and other files for this article.

Mircea Cîrnu
Department of Mathematics III, Faculty of Applied Sciences
University Politehnica of Bucharest, Romania
email: cirnumircea@yahoo.com

Return to the EJDE web page