Estimates on the Growth of Meromorphic Solutions of Linear Differential\n Equations with density conditions

2013/11/07 by Yik‐Man Chiang, Chiang, Yik-Man
Mathematics · #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.1311.1874

Abstract

We give an alternative and simpler method for getting pointwise estimate of\nmeromorphic solutions of homogeneous linear differential equations with\ncoefficients meromorphic in a finite disk or in the open plane originally\nobtained by Hayman and the author. In particular, our estimates generally give\nbetter upper bounds for higher order derivatives of the meromorphic solutions\nunder consideration, are valid, however, outside an exceptional set of finite\nlogarithmic density.\n The estimates again show that the growth of meromorphic solutions with a\npositive deficiency at infinity can be estimated in terms of initial conditions\nof the solution at or near the origin and the characteristic functions of the\ncoefficients.\n

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