The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (150 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 26, Issue 4, 2007, pp. 481–494
DOI: 10.4171/ZAA/1338

Published online: 2007-12-31

Linear q-Difference Equations

M.H. Abu Risha[1], M.H. Annaby[2], Mourad E. H. Ismail[3] and Z.S. Mansour[4]

(1) Cairo University, Egypt
(2) Cairo University, Egypt
(3) University of Central Florida, Orlando, United States
(4) Cairo University, Egypt

We prove that a linear q-difference equation of order n has a fundamental set of n-linearly independent solutions. A q-type Wronskian is derived for the n-th order case extending the results of Swarttouw--Meijer (1994) in the regular case. Fundamental systems of solutions are constructed for the n-th order linear q-difference equation with constant coefficients. A basic analog of the method of variation of parameters is established.

Keywords: q-Difference equations, q-Wronskian, q-type Liouville's formula

Abu Risha M.H., Annaby M.H., Ismail Mourad, Mansour Z.S.: Linear q-Difference Equations. Z. Anal. Anwend. 26 (2007), 481-494. doi: 10.4171/ZAA/1338