대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제57권4호
  • /
  • Pages.991-1002
  • /
  • 2020
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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EXISTENCE OF TRANSCENDENTAL MEROMORPHIC SOLUTIONS ON SOME TYPES OF NONLINEAR DIFFERENTIAL EQUATIONS

  • Hu, Peichu (School of Mathematics Shandong University) ;
  • Liu, Manli (School of Mathematics Shandong University)
  • 투고 : 2019.07.23
  • 심사 : 2019.11.06
  • 발행 : 2020.07.31
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초록

We show that when n > m, the following delay differential equation fn(z)f'(z) + p(z)(f(z + c) - f(z))m = r(z)eq(z) of rational coefficients p, r doesn't admit any transcendental entire solutions f(z) of finite order. Furthermore, we study the conditions of α1, α2 that ensure existence of transcendental meromorphic solutions of the equation fn(z) + fn-2(z)f'(z) + Pd(z, f) = p1(z)eα1(z) + p2(z)eα2(z). These results have improved some known theorems obtained most recently by other authors.

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과제정보

The authors would like to thank the referees for a careful reading of the manuscript and valuable comments and to China Scholarship Council (State Scholarship Fund No. 201906220075) for its financial support.

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