We establish the existence and uniqueness of a holomorphic solution to an implicit linear q-difference equation in a Banach space. We consider holomorphic solutions in a neighborhood of zero if |q| < 1 and entire solutions if |q| > 1. The solutions are expressed an an explicit form. The case q = 0 is separately considered.
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Translated from Problemy Matematicheskogo Analiza 107, 2020, pp. 15-22.
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Gefter, S.L., Piven’, A.L. Implicit Linear q-Difference Equations in Banach Spaces. J Math Sci 251, 787–796 (2020). https://doi.org/10.1007/s10958-020-05129-w
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DOI: https://doi.org/10.1007/s10958-020-05129-w