Solutions to some generalized Fermat-type differential-difference equations
The main purpose of this article is to study Fermat-type complex differential-difference equations $ f^{(k)}(z)^{2}+[\alpha f(z+c)-\beta f(z)]^{2} = R(z) $. Our results improve some results due to Wang–Xu–Tu [AIMS. Mathematics, 2020], Zhang [Bull. Korean. Math. Soc, 2018], and Long–Qin [Applied Math...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241643 |
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| author | Zhiyong Xu Junfeng Xu |
| author_facet | Zhiyong Xu Junfeng Xu |
| author_sort | Zhiyong Xu |
| collection | DOAJ |
| description | The main purpose of this article is to study Fermat-type complex differential-difference equations $ f^{(k)}(z)^{2}+[\alpha f(z+c)-\beta f(z)]^{2} = R(z) $. Our results improve some results due to Wang–Xu–Tu [AIMS. Mathematics, 2020], Zhang [Bull. Korean. Math. Soc, 2018], and Long–Qin [Applied Mathematics-A Journal of Chinese Universities, 2024]. Moreover, we provide some examples to show the existence of the solutions. |
| format | Article |
| id | doaj-art-6084ce5339f84c9496c7f2b508d5aadb |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-6084ce5339f84c9496c7f2b508d5aadb2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912344883450310.3934/math.20241643Solutions to some generalized Fermat-type differential-difference equationsZhiyong Xu0Junfeng Xu1School of Mathematics and Computational Sciences, Wuyi University, Jiangmen 529000, Guangdong, ChinaSchool of Mathematics and Computational Sciences, Wuyi University, Jiangmen 529000, Guangdong, ChinaThe main purpose of this article is to study Fermat-type complex differential-difference equations $ f^{(k)}(z)^{2}+[\alpha f(z+c)-\beta f(z)]^{2} = R(z) $. Our results improve some results due to Wang–Xu–Tu [AIMS. Mathematics, 2020], Zhang [Bull. Korean. Math. Soc, 2018], and Long–Qin [Applied Mathematics-A Journal of Chinese Universities, 2024]. Moreover, we provide some examples to show the existence of the solutions.https://www.aimspress.com/article/doi/10.3934/math.20241643meromorphic functionsfermat-type equationdifferential polynomialsnevanlinna theorydifferential-difference equation |
| spellingShingle | Zhiyong Xu Junfeng Xu Solutions to some generalized Fermat-type differential-difference equations AIMS Mathematics meromorphic functions fermat-type equation differential polynomials nevanlinna theory differential-difference equation |
| title | Solutions to some generalized Fermat-type differential-difference equations |
| title_full | Solutions to some generalized Fermat-type differential-difference equations |
| title_fullStr | Solutions to some generalized Fermat-type differential-difference equations |
| title_full_unstemmed | Solutions to some generalized Fermat-type differential-difference equations |
| title_short | Solutions to some generalized Fermat-type differential-difference equations |
| title_sort | solutions to some generalized fermat type differential difference equations |
| topic | meromorphic functions fermat-type equation differential polynomials nevanlinna theory differential-difference equation |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241643 |
| work_keys_str_mv | AT zhiyongxu solutionstosomegeneralizedfermattypedifferentialdifferenceequations AT junfengxu solutionstosomegeneralizedfermattypedifferentialdifferenceequations |