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

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  • Si Min Liu
  • Hong Yan Xu
  • Stanislaw Migorski

Abstract

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∂2f1z1,z2/∂z12+β∂2f1z1,z2/∂z22n1+f2z1+c1,z2+c2m1=1α∂2f2z1,z2/∂z12+β∂2f2z1,z2/∂z22n2+f1z1+c1,z2+c2m2=1 and ∂2f1z1,z2/∂z122+f2z1+c1,z2+c22=1∂2f2z1,z2/∂z122+f1z1+c1,z2+c22=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.

Suggested Citation

  • Si Min Liu & Hong Yan Xu & Stanislaw Migorski, 2021. "Entire Solutions for Complex Systems of the Second-Order Partial Differential Difference Equations of Fermat Type," Journal of Mathematics, Hindawi, vol. 2021, pages 1-14, January.
    • Handle: RePEc:hin:jjmath:4207579
    DOI: 10.1155/2021/4207579
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