Entire Solutions for Complex Systems of the Second-Order Partial Differential Difference Equations of Fermat Type | Zendy

Si Min Liu | Zendy; Hong Yan Xu | Zendy

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Entire Solutions for Complex Systems of the Second-Order Partial Differential Difference Equations of Fermat Type

Author(s) -

Si Min Liu,

Hong Yan Xu

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/4207579

Subject(s) - mathematics , order (exchange) , type (biology) , fermat's last theorem , partial differential equation , differential equation , mathematical analysis , pure mathematics , ecology , finance , economics , biology

This article is mainly concerned with the existence and the forms of entire solutions for several systems of the second-order partial differential difference equations of Fermat type α ∂ 2 f 1 z 1 , z 2 / ∂ z 1 2 + β ∂ 2 f 1 z 1 , z 2 / ∂ z 2 2 n 1 + f 2 z 1 + c 1 , z 2 + c 2 m 1 = 1 α ∂ 2 f 2 z 1 , z 2 / ∂ z 1 2 + β ∂ 2 f 2 z 1 , z 2 / ∂ z 2 2 n 2 + f 1 z 1 + c 1 , z 2 + c 2 m 2 = 1 and ∂ 2 f 1 z 1 , z 2 / ∂ z 1 2 2 + f 2 z 1 + c 1 , z 2 + c 2 2 = 1 ∂ 2 f 2 z 1 , z 2 / ∂ z 1 2 2 + f 1 z 1 + c 1 , z 2 + c 2 2 = 1 . Our results about the existence and the forms of solutions for these systems generalize the previous theorems given by Xu and Cao, Gao, Liu, and Yang. In addition, we give some examples to explain the existence of solutions of this system in each case.

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