The possible orders of growth of solutions to certain linear differential equations near a singular point
The author considers linear differential equations where the coefficients are polynomials of \(1/(z-z_0)\), and is looking for possible orders of the growth of solutions in the class of analytic functions in the punctured extended complex plane \(\overline{\mathbb C}\setminus \{z_0\}\). The substitution \(w=1/(z-z_0)\) reduces the question to the problem on possible orders of growth of entire solutions, which is completely solved in [\textit{G. G. Gundersen} et al., Trans. Am. Math. Soc. 350, No. 3, 1225--1247 (1998; Zbl 0893.34003)].
growth of solutions near a singular point
scientific article; zbMATH DE number 6813435
scientific article