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.
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M.H. Abu Risha, M.H. Annaby, Z.S. Mansour, Mourad E. H. Ismail, Linear <em>q</em>-Difference Equations. Z. Anal. Anwend. 26 (2007), no. 4, pp. 481–494DOI 10.4171/ZAA/1338