Uniqueness of meromorphic solutions sharing values with a meromorphic function to w(z+1)w(z−1)=h(z)wm(z) $w(z + 1)w(z - 1) = h(z)w^{m}(z)$
Abstract For the nonlinear difference equations of the form w(z+1)w(z−1)=h(z)wm(z), $$ w(z + 1)w(z - 1) = h(z)w^{m}(z), $$ where h(z) $h(z)$ is a nonzero rational function and m=±2,±1,0 $m = \pm 2, \pm 1,0$, we show that its transcendental meromorphic solution is mainly determined by its zeros, 1-va...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2308-9 |
| Summary: | Abstract For the nonlinear difference equations of the form w(z+1)w(z−1)=h(z)wm(z), $$ w(z + 1)w(z - 1) = h(z)w^{m}(z), $$ where h(z) $h(z)$ is a nonzero rational function and m=±2,±1,0 $m = \pm 2, \pm 1,0$, 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. |
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| ISSN: | 1687-1847 |