Some results for complex partial q-difference equations in ℂ n
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Yue Wang
Abstract
Using the Nevanlinna theory of the value distribution of meromorphic functions, the value distribution of complex partial q-difference polynomials of meromorphic functions of zero order is investigated. The existence of meromorphic solutions of some types of systems of complex partial q-difference equations in
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11171013
Award Identifier / Grant number: 11461054
Funding source: Natural Science Foundation of Hebei Province
Award Identifier / Grant number: A2015207007
Funding statement: The project was supported by the National Natural Science Foundation of China (11171013, 11461054) and supported by Natural Science Foundation of Hebei Province (A2015207007) and supported by Key Project of Science and Research of Hebei University of Economics and Business (2017KYZ04).
References
[1] D. C. Barnett, R. G. Halburd, W. Morgan and R. J. Korhonen, Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 3, 457–474. 10.1017/S0308210506000102Search in Google Scholar
[2] Z. X. Chen, Z. B. Huang and R. R. Zhang, On difference equations relating to gamma function, Acta Math. Sci. Ser. B Engl. Ed. 31 (2011), no. 4, 1281–1294. 10.1016/S0252-9602(11)60315-9Search in Google Scholar
[3]
Y.-M. Chiang and S.-J. Feng,
On the Nevanlinna characteristic of
[4] L. Y. Gao, The growth order of solutions of systems of complex difference equations, Acta Math. Sci. Ser. B Engl. Ed. 33 (2013), no. 3, 814–820. 10.1016/S0252-9602(13)60040-5Search in Google Scholar
[5] L. Y. Gao, On admissible solutions of two types of systems of differential equations in the complex plane, Acta Math. Sinica (Chin. Ser.) 43 (2000), no. 1, 149–156. Search in Google Scholar
[6] L. Y. Gao, Systems of complex difference equations of Malmquist type, Acta Math. Sinica (Chin. Ser.) 55 (2012), no. 2, 293–300. Search in Google Scholar
[7] L. Y. Gao, Solutions of complex higher-order difference equations, Acta Math. Sinica (Chin. Ser.) 56 (2013), no. 4, 451–458. Search in Google Scholar
[8] L. Y. Gao, Meromorphic solutions to a type of complex difference equations, Chinese Ann. Math. Ser. A 35 (2014), no. 2, 193–202. Search in Google Scholar
[9] R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477–487. 10.1016/j.jmaa.2005.04.010Search in Google Scholar
[10] R. Korhonen, A difference Picard theorem for meromorphic functions of several variables, Comput. Methods Funct. Theory 12 (2012), no. 1, 343–361. 10.1007/BF03321831Search in Google Scholar
[11] I. Laine and C.-C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 556–566. 10.1112/jlms/jdm073Search in Google Scholar
[12] I. Laine and C.-C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 8, 148–151. 10.3792/pjaa.83.148Search in Google Scholar
[13]
Z. H. Tu,
Some Malmquist-type theorems of partial differential equations on
[14] H. X. Yi and C. C. Yang, Theory of the Uniqueness of Meromorphic Functions, Science Press, Beijing, 1995. Search in Google Scholar
[15] Z.-T. Wen, The q-difference theorems for meromorphic functions of several variables, Abstr. Appl. Anal. 2014 (2014), Article ID 736021. 10.1155/2014/736021Search in Google Scholar
[16]
J. L. Zhang and R. Korhonen,
On the Nevanlinna characteristic of
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
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Some results for complex partial q-difference equations in
Articles in the same Issue
- Frontmatter
- (σ,τ)-*-Jordan ideals in *-prime rings
- Ruled surfaces generated by elliptic cylindrical curves in the isotropic space
- On the convergence of difference schemes for the generalized BBM–Burgers equation
- A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces
- On absolute Riesz summability factors of infinite series and their application to Fourier series
- A new set of Sheffer–Bell polynomials and logarithmic numbers
- FS-coalgebras and crossed coproducts
- On duality for a second-order multiobjective fractional programming problem involving type-I functions
- Hardy’s inequality on Hardy–Morrey spaces
- Some applications of degenerate poly-Bernoulli numbers and polynomials
- On multivalued stochastic integral equations driven by semimartingales
- Group-groupoid actions and liftings of crossed modules
- New subclasses of analytic functions defined by convolution involving the hypergeometric function and the Owa–Srivastava operator
- On groups with action on itself
-
Some results for complex partial q-difference equations in
