Existence of zero-order meromorphic solutions of certain q-difference equations
Abstract In this paper, we consider the q-difference equation (f(qz)+f(z))(f(z)+f(z/q))=R(z,f), $$ \bigl(f(qz)+f(z)\bigr) \bigl(f(z)+f(z/q)\bigr)=R(z,f), $$ where R(z,f) $R(z,f)$ is rational in f and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic s...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-08-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1790-z |
| Summary: | Abstract In this paper, we consider the q-difference equation (f(qz)+f(z))(f(z)+f(z/q))=R(z,f), $$ \bigl(f(qz)+f(z)\bigr) \bigl(f(z)+f(z/q)\bigr)=R(z,f), $$ where R(z,f) $R(z,f)$ is rational in f and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic solution f(z) $f(z)$, then either f(z) $f(z)$ is a solution of a q-difference Riccati equation or the coefficients satisfy some conditions. |
|---|---|
| ISSN: | 1029-242X |