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Oscillation results for n-th order linear differential equations with meromorphic periodic coefficients

Published online by Cambridge University Press:  22 January 2016

Shun Shimomura
Shun Shimomura*
Affiliation:
Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan, shimomur@math.keio.ac.jp
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Abstract

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Consider n-th order linear differential equations with meromorphic periodic coefficients of the form w(n) + Rn-1(ez)w(n-1) + … + R1(ez)w′ + R0(ez)w = 0, n ≥ 2, where Rv(t) (0 ≤ ν ≤ n – 1) are rational functions of t. Under certain assumptions, we prove oscillation theorems concerning meromorphic solutions, which contain necessary conditions for the existence of a meromorphic solution with finite exponent of convergence of the zero-sequence. We also discuss meromorphic or entire solutions whose zero-sequences have an infinite exponent of convergence, and give a new zero-density estimate for such solutions.

Keywords

34M1034M0534M3030D35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 166 , June 2002 , pp. 55 - 82
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

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