Implicit linear \(q\)-difference equations in Banach spaces (Q2214354)

The existence of meromorphic solutions of differential, difference and \(q\)-difference equations is a challenging problem. In this paper, the authors focus on a \(q\)-difference Riccati equation defined in a Banach space, and establish the existence and uniqueness of its analytic solutions. The explicit forms of holomorphic solutions are given for \(|q|<1\), \(|q|>1\) and \(q=0\).