Asymptotics beyond all orders and analytic properties of inverse Laplace transforms of solutions (Q1330956)

The author obtains some analytic properties of inverse \(\nu\)-transform of the solution of the differential equation \[ x^{1 - r} y'(x) = f(x,y), \quad x \in \overline \mathbb{C}, \quad y \in \mathbb{C}^ n, \quad r \in\mathbb{N}, \] where the vector-valued function \(f(x,y)\) is homomorphic at \((\infty, 0) \in \overline \mathbb{C} \times \mathbb{C}^ n\).