Properties of Schwarzian difference equations
We consider the Schwarzian type difference equation $$ \Big[\frac{\Delta^{3}f(z)}{\Delta f(z)}-\frac{3}{2} \Big(\frac{\Delta^{2}f(z)}{\Delta f(z)}\Big)^{2}\Big]^{k}=R(z), $$ where R(z) is a nonconstant rational function. We study the existence of rational solutions and value distribution of tr...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Texas State University
2015-08-01
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Series: | Electronic Journal of Differential Equations |
Subjects: | |
Online Access: | http://ejde.math.txstate.edu/Volumes/2015/199/abstr.html |
Summary: | We consider the Schwarzian type difference equation
$$
\Big[\frac{\Delta^{3}f(z)}{\Delta f(z)}-\frac{3}{2}
\Big(\frac{\Delta^{2}f(z)}{\Delta f(z)}\Big)^{2}\Big]^{k}=R(z),
$$
where R(z) is a nonconstant rational function. We study the existence of
rational solutions and value distribution of transcendental meromorphic
solutions with finite order of the above equation. |
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ISSN: | 1072-6691 |