Some Properties on Complex Functional Difference Equations
We obtain some results on the transcendental meromorphic solutions of complex functional difference equations of the form ∑λ∈Iαλ(z)(∏j=0nf(z+cj)λj)=R(z,f∘p)=((a0(z)+a1(z)(f∘p)+ ⋯ +as(z) (f∘p)s)/(b0(z)+b1(z)(f∘p)+ ⋯ +bt(z)(f∘p)t)), where I is a finite set of multi-indexes λ=(λ0,λ1,…,λn), c0=0,cj∈ℂ∖{0...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/283895 |
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| author | Zhi-Bo Huang Ran-Ran Zhang |
| author_facet | Zhi-Bo Huang Ran-Ran Zhang |
| author_sort | Zhi-Bo Huang |
| collection | DOAJ |
| description | We obtain some results on the transcendental meromorphic solutions of complex functional difference equations of the form ∑λ∈Iαλ(z)(∏j=0nf(z+cj)λj)=R(z,f∘p)=((a0(z)+a1(z)(f∘p)+ ⋯ +as(z) (f∘p)s)/(b0(z)+b1(z)(f∘p)+ ⋯ +bt(z)(f∘p)t)), where I is a finite set of multi-indexes λ=(λ0,λ1,…,λn), c0=0,cj∈ℂ∖{0} (j=1,2,…,n) are distinct complex constants, p(z) is a polynomial, and αλ(z) (λ∈I), ai(z) (i=0,1,…,s), and bj(z) (j=0,1,…,t) are small meromorphic functions relative to f(z). We further investigate the above functional difference equation which has special type if its solution has Borel exceptional zero and pole. |
| format | Article |
| id | doaj-art-342260bf8e1b40f7b351b7552ffdd98d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-342260bf8e1b40f7b351b7552ffdd98d2025-08-20T03:55:06ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/283895283895Some Properties on Complex Functional Difference EquationsZhi-Bo Huang0Ran-Ran Zhang1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou 510303, ChinaWe obtain some results on the transcendental meromorphic solutions of complex functional difference equations of the form ∑λ∈Iαλ(z)(∏j=0nf(z+cj)λj)=R(z,f∘p)=((a0(z)+a1(z)(f∘p)+ ⋯ +as(z) (f∘p)s)/(b0(z)+b1(z)(f∘p)+ ⋯ +bt(z)(f∘p)t)), where I is a finite set of multi-indexes λ=(λ0,λ1,…,λn), c0=0,cj∈ℂ∖{0} (j=1,2,…,n) are distinct complex constants, p(z) is a polynomial, and αλ(z) (λ∈I), ai(z) (i=0,1,…,s), and bj(z) (j=0,1,…,t) are small meromorphic functions relative to f(z). We further investigate the above functional difference equation which has special type if its solution has Borel exceptional zero and pole.http://dx.doi.org/10.1155/2014/283895 |
| spellingShingle | Zhi-Bo Huang Ran-Ran Zhang Some Properties on Complex Functional Difference Equations Abstract and Applied Analysis |
| title | Some Properties on Complex Functional Difference Equations |
| title_full | Some Properties on Complex Functional Difference Equations |
| title_fullStr | Some Properties on Complex Functional Difference Equations |
| title_full_unstemmed | Some Properties on Complex Functional Difference Equations |
| title_short | Some Properties on Complex Functional Difference Equations |
| title_sort | some properties on complex functional difference equations |
| url | http://dx.doi.org/10.1155/2014/283895 |
| work_keys_str_mv | AT zhibohuang somepropertiesoncomplexfunctionaldifferenceequations AT ranranzhang somepropertiesoncomplexfunctionaldifferenceequations |