Bibliographic Details
| Title: |
Characterizations of transcendental entire solutions of trinomial partial differential-difference equations in ℂ2# |
| Authors: |
Xu Hong Yan, Haldar Goutam |
| Source: |
Demonstratio Mathematica, Vol 57, Iss 1, Pp 443-551 (2024) |
| Publisher Information: |
De Gruyter, 2024. |
| Publication Year: |
2024 |
| Collection: |
LCC:Mathematics |
| Subject Terms: |
functions of several complex variables, fermat-type equations, entire solutions, nevanlinna theory, 30d35, 35m30, 32w50, 39a45, Mathematics, QA1-939 |
| More Details: |
This study is devoted to exploring the existence and the precise form of finite-order transcendental entire solutions of second-order trinomial partial differential-difference equations L(f)2+2hL(f)f(z1+c1,z2+c2)+f(z1+c1,z2+c2)2=eg(z1,z2)L{(f)}^{2}+2hL(f)f\left({z}_{1}+{c}_{1},{z}_{2}+{c}_{2})+f{\left({z}_{1}+{c}_{1},{z}_{2}+{c}_{2})}^{2}={e}^{g\left({z}_{1},{z}_{2})} and L˜(f)2+2hL˜(f)(f(z1+c1,z2+c2)−f(z1,z2))+(f(z1+c1,z2+c2)−f(z1,z2))2=eg(z1,z2),\tilde{L}{(f)}^{2}+2h\tilde{L}(f)(f\left({z}_{1}+{c}_{1},{z}_{2}+{c}_{2})-f\left({z}_{1},{z}_{2}))+{(f\left({z}_{1}+{c}_{1},{z}_{2}+{c}_{2})-f\left({z}_{1},{z}_{2}))}^{2}={e}^{g\left({z}_{1},{z}_{2})}, where L(f)L(f) and L˜(f)\tilde{L}(f) are defined in (2.1) and (2.2), respectively, and g(z)g\left(z) is a polynomial in C2{{\mathbb{C}}}^{2}. Our results are the extensions of some of the previous results of Liu et al. Also, we exhibit a series of examples to explain that the forms of transcendental entire solutions of finite-order in our results are precise. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
2391-4661 |
| Relation: |
https://doaj.org/toc/2391-4661 |
| DOI: |
10.1515/dema-2024-0052 |
| Access URL: |
https://doaj.org/article/608c5a8ff2d740d0bdc210bb53b7fc0b |
| Accession Number: |
edsdoj.608c5a8ff2d740d0bdc210bb53b7fc0b |
| Database: |
Directory of Open Access Journals |
