Solutions for systems of complex Fermat type partial differential-difference equations with two complex variables

Hong Li; Keyu Zhang; Hongyan Xu; Hong Li; Keyu Zhang; Hongyan Xu

doi:10.3934/math.2021685

AIMS Mathematics

2021, Volume 6, Issue 11: 11796-11814. doi: 10.3934/math.2021685

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Solutions for systems of complex Fermat type partial differential-difference equations with two complex variables

Hong Li ^1,2,
Keyu Zhang ^{3
,
,},
Hongyan Xu ^{1,4
,
,}

1.
Office of Academic Research, Gannan Normal University, Ganzhou, Jiangxi 341000, China
2.
School of Psychology, Jiangxi Normal University, Nanchang 330022, China
3.
School of Mathematics, Qilu Normal university, Jinan, Shandong 250200, China
4.
School of Mathematics and Computer Science, Shangrao Normal University, Shangrao, Jiangxi 334001, China

Received: 23 May 2021 Accepted: 28 July 2021 Published: 13 August 2021
MSC : 39A45, 35M10, 39A14, 30D35

By making use of the Nevanlinna theory and difference Nevanlinna theory of several complex variables, we investigate some properties of the transcendental entire solutions for several systems of partial differential difference equations of Fermat type, and obtain some results about the existence and the forms of transcendental entire solutions of the above systems, which improve and generalize the previous results given by Cao, Gao, Liu ^[5,24,39]. Some examples are given show that there exist some significant differences in the forms of transcendental entire solutions with finite order of the systems of equations with between several complex variables and a single complex variable.
- entire solution,
- Nevanlinna theory,
- system of partial differential-difference equations,
- existence
Citation: Hong Li, Keyu Zhang, Hongyan Xu. Solutions for systems of complex Fermat type partial differential-difference equations with two complex variables[J]. AIMS Mathematics, 2021, 6(11): 11796-11814. doi: 10.3934/math.2021685

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Abstract

By making use of the Nevanlinna theory and difference Nevanlinna theory of several complex variables, we investigate some properties of the transcendental entire solutions for several systems of partial differential difference equations of Fermat type, and obtain some results about the existence and the forms of transcendental entire solutions of the above systems, which improve and generalize the previous results given by Cao, Gao, Liu ^[5,24,39]. Some examples are given show that there exist some significant differences in the forms of transcendental entire solutions with finite order of the systems of equations with between several complex variables and a single complex variable.

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