A study of solutions for several classes of systems of complex nonlinear partial differential difference equations in ℂ <sup>2</sup>
Abstract This article is devoted to describing the entire solutions of several systems of the first-order nonlinear partial differential difference equations (PDDEs). Using the Nevanlinna theory and the Hadamard factorization theory of meromorphic functions, we establish some interesting results to reveal the existence and the forms of the finite-order transcendental entire solutions of several systems of the first-order nonlinear PDDEs: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mtable displaystyle="true"> <m:mtr> <m:mtd columnalign="left"> <m:mfenced open="{" close=""> <m:mrow> <m:mtable displaystyle="true"> <m:mtr> <m:mtd columnalign="left"> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>a</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:mrow> </m:msub> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:msub> <m:mrow> <m:mi>m</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign="left"> <m:mi>g</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>c</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub>
Authors
- Yu Bin Chen
- Xin Jiao (ORCID: https://orcid.org/0000-0002-0761-3972)
- Hong Yan Xu (ORCID: https://orcid.org/0009-0008-7031-8248)
Institutions
- Suqian University
Publication Details
- Journal
- Demonstratio Mathematica
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1515/dema-2025-0119
- Citations
- 2
- Primary Topic
- Meromorphic and Entire Functions
- Type
- article
- Field-Weighted Citation Impact
- 7.45