대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권3호
  • /
  • Pages.597-610
  • /
  • 2024
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON THE GROWTH OF ALGEBROID SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

  • Manli Liu (Department of Mathematics South China Agricultural University) ;
  • Linlin Wu (School of Mathematics Qilu Normal University)
  • 투고 : 2023.05.03
  • 심사 : 2023.08.07
  • 발행 : 2024.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with algebroid solutions and obtains two results, which extend the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [4].

키워드

과제정보

This work was partially supported by the National Natural Science Foundation of China (No.12301095), Topics on Baisc and Applied Basic research of Guangzhou in 2023 (NO.2023A04J0648).

참고문헌

  1. S. B. Bank, On the growth of solutions of algebraic differential equations, Trans. Amer. Math. Soc. 240 (1978), 195-212. https://doi.org/10.2307/1998813
  2. S. B. Bank and R. P. Kaufman, On the growth of meromorphic solutions of the differential equation (y')m = R(z, y), Acta Math. 144 (1980), no. 3-4, 223-248. https://doi.org/10.1007/BF02392124
  3. S. B. Bank and I. Laine, On the zeros of meromorphic solutions and second-order linear differential equations, Comment. Math. Helv. 58 (1983), no. 4, 656-677. https://doi.org/10.1007/BF02564659
  4. L. Gao, On admissible solutions of two types of systems of differential equations in the complex plane, Acta Math. Sinica (Chinese Ser.) 43 (2000), no. 1, 149-156.
  5. L. Gao, On the growth of solutions of higher-order algebraic differential equations, Acta Math. Sci. Ser. B (Engl. Ed.) 22 (2002), no. 4, 459-465. https://doi.org/10.1016/S0252-9602(17)30318-1
  6. Y. Z. He and I. Laine, On the growth of algebroid solutions of algebraic differential equations, Math. Scand. 58 (1986), no. 1, 125-138.
  7. Y. Z. He and X. X. Xiao, Algebroid Functions and Ordinary Differential Equations, Beijing, Science Press, 1988.
  8. D. Sun, Y. Huo, and X. Zhang, General algebroid function and its application, Acta Math. Sci. Ser. B (Engl. Ed.) 36 (2016), no. 1, 283-294. https://doi.org/10.1016/S0252-9602(15)30095-3
  9. Y. Tan and Q. Zhang, Borel directions and the uniqueness of algebroid functions dealing with multiple values, Studia Sci. Math. Hungar. 58 (2021), no. 1, 104-118. https://doi.org/10.1556/012.2021.58.1.1488
  10. N. Toda, On the conjecture of Gackstatter and Laine concerning the differential equation (w')n =Σmj=0 aj(z)wj, Kodai Math. J. 6 (1983), no. 2, 238-249. https://doi.org/10.2996/kmj/1138036720
  11. N. Toda, On the growth of nonadmissible solutions of the differential equation (w')n = Σmj=0 ajwj, Kodai Math. J. 7 (1984), no. 3, 293-303. https://doi.org/10.2996/kmj/1138036952
  12. X. Z. Xiao and Y. Z. He, Meromorphic and algebroid solutions of higher-order algebraic differential equations, Sci. Sinica Ser. A 26 (1983), no. 10, 1034-1043.
  13. K. Yosida, On algebroid solutions of ordinary differential equations, Japan J. Math. 10 (1934), 119-208.
  14. P. Zhang and P. Hu, On uniqueness for algebroid functions of finite order, Acta Math. Sci. Ser. B (Engl. Ed.) 35 (2015), no. 3, 630-638. https://doi.org/10.1016/S0252-9602(15)30009-6