| Title:
|
Existence of entire solutions of nonlinear difference equations (English) |
| Author:
|
Liu, Kai |
| Author:
|
Yang, Lianzhong |
| Author:
|
Liu, Xinling |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
565-576 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we obtain that there are no transcendental entire solutions with finite order of some nonlinear difference equations of different forms. (English) |
| Keyword:
|
entire functions |
| Keyword:
|
difference equations |
| Keyword:
|
finite order |
| MSC:
|
30D35 |
| MSC:
|
39B32 |
| idZBL:
|
Zbl 1249.30102 |
| idMR:
|
MR2905424 |
| DOI:
|
10.1007/s10587-011-0075-1 |
| . |
| Date available:
|
2011-06-06T10:56:33Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141554 |
| . |
| Reference:
|
[1] Bergweiler, W., Langley, J. K.: Zeros of difference of meromorphic functions.Math. Proc. Camb. Philos. Soc. 142 (2007), 133-147. MR 2296397, 10.1017/S0305004106009777 |
| Reference:
|
[2] Chiang, Y.-M., Feng, S.-J.: On the Nevanlinna characteristic of $f(z+\eta)$ and difference equations in the complex plane.Ramanujan. J. 16 (2008), 105-129. Zbl 1152.30024, MR 2407244, 10.1007/s11139-007-9101-1 |
| Reference:
|
[3] Chen, Z. X., Shon, K. H.: Estimates for the zeros of differences of meromorphic functions.Sci. China, Ser. A 52 (2009), 2447-2458. Zbl 1181.30016, MR 2566657, 10.1007/s11425-009-0159-7 |
| Reference:
|
[4] Clunie, J.: On integral and meromorphic functions.J. Lond. Math. Soc. 37 (1962), 17-27. Zbl 0104.29504, MR 0143906, 10.1112/jlms/s1-37.1.17 |
| Reference:
|
[5] Gross, F.: On the equation $f^{n}+g^{n}=1$.Bull. Am. Math. Soc. 72 (1966), 86-88. MR 0185125, 10.1090/S0002-9904-1966-11429-5 |
| Reference:
|
[6] Halburd, R. G., Korhonen, R. J.: Difference analogue of the lemma on the logarithmic derivative with applications to difference equations.J. Math. Anal. Appl. 314 (2006), 477-487. Zbl 1085.30026, MR 2185244, 10.1016/j.jmaa.2005.04.010 |
| Reference:
|
[7] Halburd, R. G., Korhonen, R. J.: Nevanlinna theory for the difference operator.Ann. Acad. Sci. Fenn., Math. 31 (2006), 463-478. Zbl 1108.30022, MR 2248826 |
| Reference:
|
[8] Halburd, R. G., Korhonen, R. J., Tohge, K.: Holomorphic cures with shift-invariant hyperplane preimages.. |
| Reference:
|
[9] Laine, I.: Nevanlinna Theory and Complex Differential Equations.Walter de Gruyter Berlin (1992). Zbl 0784.30002, MR 1207139 |
| Reference:
|
[10] Laine, I., Yang, C. C.: Clunie theorems for difference and $q$-difference polynomials.J. Lond. Math. Soc. 76 (2007), 556-566. Zbl 1132.30013, MR 2377111, 10.1112/jlms/jdm073 |
| Reference:
|
[11] Liu, K., Laine, I.: A note on value distribution of difference polynomials.Bull. Aust. Math. Soc. 81 (2010), 353-360. Zbl 1201.30035, MR 2639851, 10.1017/S000497270900118X |
| Reference:
|
[12] Liu, K.: Zeros of difference polynomials of meromorphic functions.Result. Math. 57 (2010), 365-376. Zbl 1201.30036, MR 2651120, 10.1007/s00025-010-0034-4 |
| Reference:
|
[13] Liu, K.: Meromorphic functions sharing a set with applications to difference equations.J. Math. Anal. Appl. 359 (2009), 384-393. Zbl 1177.30035, MR 2542182, 10.1016/j.jmaa.2009.05.061 |
| Reference:
|
[14] Mohon'ko, A. Z.: The Nevanlinna characteristics of certain meromorphic functions.Teor. Funktsii Funktsional. Anal. i Prilozhen. 14 (1971), 83-87 Russian. MR 0298006 |
| Reference:
|
[15] Whittaker, J. M.: Interpolatory Function Theory. Cambridge Tracts in Math. a. Math. Phys. 33.Cambridge University Press London (1935). |
| Reference:
|
[16] Yang, C.-C., Laine, I.: On analogies between nonlinear difference and differential equations.Proc. Japan Acad., Ser. A. 86 (2010), 10-14. Zbl 1207.34118, MR 2598818 |
| Reference:
|
[17] Yang, C.-C., Yi, H.-X.: Uniqueness Theory of Meromorphic Functions. Mathematics and its Applications 557.Kluwer Academic Publishers/Science Press Dordrecht/Beijing (2003). MR 2105668 |
| . |
