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.
|Number of pages||28|
|Journal||Nagoya Mathematical Journal|
|Publication status||Published - 2002 Jun 1|
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