JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (12): 34-44.doi: 10.6040/j.issn.1671-9352.0.2021.785

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Entire solutions of two types of nonlinear differential-difference equations

GAO Zhen-guang   

  1. College of Information Science and Technology, Jinan University, Guangzhou 510632, Guangdong, China
  • Published:2022-12-05

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Abstract: Using Nevanlinna's value distribution theory, this paper investigates the existence of entire solutions with finite order of two types of nonlinear differential-difference equations of the forms f n+ωf n-1f '+b(f ')n+qeQf(z+c)=uev and f n+ω1f n-1f '+ω2(f ')n+qeQf(z+c)=p1eλ1z+p2eλ2z, and obtains two results. Examples are provided to show that the results obtained in this paper, in a sense, are best possible.

Key words: nonlinear differential-difference equation, entire solution, dominant term, order of growth

CLC Number: 

  • O174.52
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