## Taiwanese Journal of Mathematics

### ON ENTIRE SOLUTIONS OF A CERTAIN TYPE OF NONLINEAR DIFFERENTIAL AND DIFFERENCE EQUATIONS

#### Abstract

In this paper, we investigate some analogous results on the existence of entire solutions of a certain type of nonlinear differential and differential-difference equations of the following form $$f^n(z) + P_d(f) = p_1(z) e^{\alpha_1 z} + p_2(z) e^{\alpha_2 z},$$ where $P_d(f)$ is a differential polynomial or differential-difference polynomial in $f(z)$. And we find out its entire solutions or prove that it has no entire solution for some special $P_d(f)$.

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 5 (2011), 2145-2157.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406427

Digital Object Identifier
doi:10.11650/twjm/1500406427

Mathematical Reviews number (MathSciNet)
MR2880397

Zentralblatt MATH identifier
1242.30025

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 34M10: Oscillation, growth of solutions

#### Citation

Zhang, Jie; Liao, Liang-Wen. ON ENTIRE SOLUTIONS OF A CERTAIN TYPE OF NONLINEAR DIFFERENTIAL AND DIFFERENCE EQUATIONS. Taiwanese J. Math. 15 (2011), no. 5, 2145--2157. doi:10.11650/twjm/1500406427. https://projecteuclid.org/euclid.twjm/1500406427

#### References

• J. Clunie, On integral and meromorphic functions, J. London Math. Soc., 37 (1962), 17-27.
• W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
• I. Lanie and C. C. Yang, Clunie theorems for difference and q-difference polynomials. J. London. Math. Soc., 76 (2007), 556-566.
• P. Li and C. C. Yang, On the nonexistence of entire solutions of certain type of nonlinear differential equations, J. Math. Appl., 320 (2006), 827-835.
• C. C. Yang, A generalization of a theorem of P.Montel on entire functions, Proc. Amer. Math. Soc., 26 (1970), 332-334.
• C. C. Yang and P. Li, On the transcendental solutions of a certain type of nonlinear differential equations, Arch. Math., 82 (2004), 442-448.
• C. C. Yang and H. X. Yi, Uniqueness Theory of meromorphic functions, Science Press, Beijing, Second Printed in 2006.
• L. Yang, Value Distribution Theory, Springer-Verlag & Science Press, Berlin, 1993.