### 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)} + ⋯ + R_{1}(e^{z})w′ + R_{0}(e^{z})w = 0, n ≥ 2, where R_{ν}(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.

Original language | English |
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Pages (from-to) | 55-82 |

Number of pages | 28 |

Journal | Nagoya Mathematical Journal |

Volume | 166 |

Publication status | Published - 2002 Jun |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Nagoya Mathematical Journal*,

*166*, 55-82.

**Oscillation results for n-th order linear differential equations with meromorphic periodic coefficients.** / Shimomura, Shun.

Research output: Contribution to journal › Article

*Nagoya Mathematical Journal*, vol. 166, pp. 55-82.

}

TY - JOUR

T1 - Oscillation results for n-th order linear differential equations with meromorphic periodic coefficients

AU - Shimomura, Shun

PY - 2002/6

Y1 - 2002/6

N2 - 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 Rν(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.

AB - 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 Rν(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.

UR - http://www.scopus.com/inward/record.url?scp=0036620877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036620877&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036620877

VL - 166

SP - 55

EP - 82

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -