Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2
The purpose of this article is to give the details of finding the transcendental entire solutions with finite order for the systems of nonlinear partial differential-difference equations ∂f1z1,z2/∂z1+∂f1z1,z2/∂z2n1+P1zf2z1+c1,z2+c2m1=Q1z,∂f1z1,z2/∂z1+∂f1z1,z2/∂z2n2+P2zf1z1+c1,z2+c2m2=Q2z, where P1z,...
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| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/5424284 |
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| author | Hong Li Hong Yan Xu |
| author_facet | Hong Li Hong Yan Xu |
| author_sort | Hong Li |
| collection | DOAJ |
| description | The purpose of this article is to give the details of finding the transcendental entire solutions with finite order for the systems of nonlinear partial differential-difference equations ∂f1z1,z2/∂z1+∂f1z1,z2/∂z2n1+P1zf2z1+c1,z2+c2m1=Q1z,∂f1z1,z2/∂z1+∂f1z1,z2/∂z2n2+P2zf1z1+c1,z2+c2m2=Q2z, where P1z,P2z,Q1z,andQ2z are polynomials in ℂ2; n1,n2,m1,and m2 are positive integers, and c=c1,c2∈ℂ2. We obtain that there exist some pairs of the transcendental entire solutions of finite order for the above system, which is a very powerful supplement to the previous theorems given by Xu and Cao and Xu and Yang. |
| format | Article |
| id | doaj-art-976fea45dab54169a58f2af9a82e8aa0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-976fea45dab54169a58f2af9a82e8aa02025-08-20T03:37:09ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/54242845424284Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2Hong Li0Hong Yan Xu1School of Psychology, Jiangxi Normal University, Nanchang 330022, ChinaSchool of Psychology, Jiangxi Normal University, Nanchang 330022, ChinaThe purpose of this article is to give the details of finding the transcendental entire solutions with finite order for the systems of nonlinear partial differential-difference equations ∂f1z1,z2/∂z1+∂f1z1,z2/∂z2n1+P1zf2z1+c1,z2+c2m1=Q1z,∂f1z1,z2/∂z1+∂f1z1,z2/∂z2n2+P2zf1z1+c1,z2+c2m2=Q2z, where P1z,P2z,Q1z,andQ2z are polynomials in ℂ2; n1,n2,m1,and m2 are positive integers, and c=c1,c2∈ℂ2. We obtain that there exist some pairs of the transcendental entire solutions of finite order for the above system, which is a very powerful supplement to the previous theorems given by Xu and Cao and Xu and Yang.http://dx.doi.org/10.1155/2021/5424284 |
| spellingShingle | Hong Li Hong Yan Xu Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2 Journal of Function Spaces |
| title | Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2 |
| title_full | Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2 |
| title_fullStr | Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2 |
| title_full_unstemmed | Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2 |
| title_short | Notes on Solutions for Some Systems of Complex Functional Equations in ℂ2 |
| title_sort | notes on solutions for some systems of complex functional equations in c2 |
| url | http://dx.doi.org/10.1155/2021/5424284 |
| work_keys_str_mv | AT hongli notesonsolutionsforsomesystemsofcomplexfunctionalequationsinc2 AT hongyanxu notesonsolutionsforsomesystemsofcomplexfunctionalequationsinc2 |