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Uniqueness of meromorphic solutions sharing values with a meromorphic function to \(w(z + 1)w(z - 1) = H(z)w^m(z)\). (English) Zbl 07254386
Summary: For the nonlinear difference equations of the form \(w(z + 1)w(z - 1) = h(z)w^m(z),\) where \(h(z)\) is a nonzero rational function and \(m = \pm 2, \pm 1,0\), we show that its transcendental meromorphic solution is mainly determined by its zeros, 1-value points and poles except for some special cases. Examples for the sharpness of these results are given.
MSC:
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
39B32 Functional equations for complex functions
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