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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.
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
39B32 Functional equations for complex functions
Full Text: DOI
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