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Estimates on the growth of meromorphic solutions of linear differential equations. (English) Zbl 1057.34110
The paper is devoted to pointwise estimates on meromorphic solutions of linear differential equations with coefficients meromorphic on a finite disc or on an open plane. It is shown that the growth of suitable solutions can be estimated sharply in terms of initial conditions of the solution at or near the origin and the characteristic functions of the coefficients. The proof is based on the construction of a path consisting of a ray and a circle on which the coefficients are all bounded in terms of the sum of their characteristic functions on a larger circle.
MSC:
34M10Oscillation, growth of solutions (ODE in the complex domain)
34M05Entire and meromorphic solutions (ODE)