Interval estimation on hyper-order of meromorphic solutions of complex linear differential equations with uncertain coefficients

The authors address the complex oscillation problems of all solutions of homogenous linear differential equations with meromorphic coefficients. Sufficient conditions for estimating the growth of meromorphic solution with infinite order have been proposed based on Nevanlinna value distribution theory. Compared with the existing results, the proposed hyper-order of all meromorphic solutions with infinite order can be estimated in terms of a bounded interval which includes information of order of growth of meromorphic functions and meromorphic polynomial coefficients.