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Zeros of meromorphic solutions to second-order differential equations with meromorphic coefficients. (Chinese) Zbl 1011.34072

Here, the author considers equations of the form \[ f''+ B(z)= H(z),\tag{\(*\)} \] where \(B(z)\) is a rational function having a pole of order \(n\geq 1\) at infinity, and \(H(z)\not\equiv 0\) is a meromorphic function of finite order. For a meromorphic function \(f\), let \(\sigma(f)\) denote the order of \(f\), \(\lambda(f)\) the exponent of convergence of the sequence of zeros of \(f\), and \(\overline\lambda(f)\) the exponent of convergence of the sequence of distinct zeros of \(f\). The author proves, among other things, that all exept at most one meromoprhic solution to \((*)\) satisfy \(\overline\lambda(f)= \lambda(f)= \sigma(f)= \max\{\sigma(H),(n+2)/2\}\).

MSC:

34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
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