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On entire solutions of nonlinear difference-differential equations

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In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form fn + Q(z, f) = h, where n ≥ 2 is an integer, Q(z, f) is a differential-difference polynomial in f with polynomial coefficients, and h is a meromorphic function of order ≤ 1.

Abstract

In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form fn + Q(z, f) = h, where n ≥ 2 is an integer, Q(z, f) is a differential-difference polynomial in f with polynomial coefficients, and h is a meromorphic function of order ≤ 1.

참고문헌 (11)

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  2. J. Clunie, "On integral and meromorphic functions", J. London Math. Soc, 37, pp.17~27 (1962)
  3. R. G. Halburd, "Difference analogue of the lemma on the logarithmic derivative with applications to difference equations", J. Math. Anal. Appl, 314(2), pp.477~487 (2006)
  4. W. K. Hayman, "Meromorphic Functions" (1964), Clarendon Press
  5. J. Heittokangas, "On meromorphic solutions of certain non- linear differential equations", Bull. Austral. Math. Soc, 66(2), pp.331~343 (2002)
  6. I. Laine, "Nevanlinna Theory and Complex Differential Equations" (1993), De Gruyter
  7. I. Laine, "Clunie theorems for difference and q-difference polynomials", J. Lond. Math. Soc, 76(3), pp.556~566 (2007)
  8. P. Li, "On the nonexistence of entire solutions of certain type of nonlinear differential equations", J. Math. Anal. Appl, 302(2), pp.827~835 (2006)
  9. C. C. Yang, "On analogies between nonlinear difference and differential equations", Proc. Japan Acad. Ser. A Math. Sci, 86(1), pp.10~14 (2010)
  10. C. C. Yang, "On the transcendental solutions of a certain type of nonlinear differential equations", Arch. Math, 82(5), pp.442~448 (2004)
  11. C. C. Yang, "Estimates of the proximate function of differential polynomials", Proc. Japan Acad. Ser. A Math. Sci, 83(4), pp.50~55 (2007)

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