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.

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U2 - 10.1017/s0027763000008254

DO - 10.1017/s0027763000008254

M3 - Article

AN - SCOPUS:0036620877

VL - 166

SP - 55

EP - 82

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -