Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MEROMORPHIC SOLUTIONS OF SOME NON-LINEAR DIFFERENCE EQUATIONS WITH THREE EXPONENTIAL TERMS

  • Min-Feng Chen (School of Mathematics and Statistics Guangdong University of Foreign Studies) ;
  • Zong-Sheng Gao (LMIB & School of Mathematical Sciences Beihang University) ;
  • Xiao-Min Huang (School of Mathematics and Statistics Guangdong University of Technology)
  • Received : 2023.06.01
  • Accepted : 2023.08.29
  • Published : 2024.05.31
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Abstract

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fn(z) + Pd(z, f) = p1eα1z + p2eα2z + p3eα3z, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, pj (j = 1, 2, 3) are small meromorphic functions of f and αj (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on αj (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

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Acknowledgement

The authors would like to thank the referee for valuable suggestions to the present paper.

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