Zeitschrift für Analysis und ihre Anwendungen

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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