Nagoya Mathematical Journal

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

Shun Shimomura

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Abstract

Consider $n$-th order linear differential equations with meromorphic periodic coefficients of the form $w^{(n)}+R_{n-1}(e^{z})w^{(n-1)}+\cdots+ R_{1}(e^{z})w'+R_{0}(e^{z})w = 0$, $n \ge 2$, where $R_{\nu}(t)$ $(0 \le \nu \le n-1)$ 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.

Article information

Source
Nagoya Math. J., Volume 166 (2002), 55-82.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631733

Mathematical Reviews number (MathSciNet)
MR1908573

Zentralblatt MATH identifier
1048.34143

Subjects
Primary: 34M10: Oscillation, growth of solutions
Secondary: 30D35: Distribution of values, Nevanlinna theory

Citation

Shimomura, Shun. Oscillation results for {$n$}-th order linear differential equations with meromorphic periodic coefficients. Nagoya Math. J. 166 (2002), 55--82. https://projecteuclid.org/euclid.nmj/1114631733


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