Characterizations of transcendental entire solutions of trinomial partial differential-difference equations in ℂ2

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 and where and are defined in ( ) and ( ), respectively, and is a polynomial in . Our results are the extensions of...

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Veröffentlicht in:Demonstratio mathematica Jg. 57; H. 1; S. 443 - 551
Hauptverfasser: Xu, Hong Yan, Haldar, Goutam
Format: Journal Article
Sprache:Englisch
Veröffentlicht: De Gruyter 21.11.2024
Schlagworte:
30D35
32W50
35M30
39A45
entire solutions
Fermat-type equations
functions of several complex variables
Nevanlinna theory
ISSN:2391-4661
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Zusammenfassung: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 and where and are defined in ( ) and ( ), respectively, and is a polynomial in . 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.
ISSN:2391-4661
DOI:10.1515/dema-2024-0052