Аннотация:Let q > 1.The paper considers a linear q-difference-differential equation: it is a q-difference equation in the time variable t, and a partial differential equation in the space variable z.Under suitable conditions and by using q-Borel and q-Laplace transforms (introduced by J.-P.Ramis and C. Zhang), the authors show that if it has a formal power series solution X(t, z) one can construct an actual holomorphic solution which admits X(t, z) as a q-Gevrey asymptotic expansion of order 1.
