scholarly journals Fatou sets of entire solutions of linear differential equations

2014 ◽  
Vol 409 (1) ◽  
pp. 275-281 ◽  
Author(s):  
Zhi-Gang Huang ◽  
Jun Wang
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Entire Solutions ◽  
Fatou Sets ◽  
Linear Differential

Entire solutions of certain type of non-linear differential equations

2020 ◽  
Vol 70 (1) ◽  
pp. 87-94
Author(s):  
Bo Xue
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Nonlinear Differential Equations ◽  
Differential Polynomial ◽  
Value Distribution ◽  
Linear Differential Equations ◽  
Entire Solutions ◽  
Value Distribution Theory ◽  
Linear Differential

AbstractUtilizing Nevanlinna’s value distribution theory of meromorphic functions, we study transcendental entire solutions of the following type nonlinear differential equations in the complex plane$$\begin{array}{} \displaystyle f^{n}(z)+P(z,f,f',\ldots,f^{(t)})=P_{1}\text{e}^{\alpha_{1}z}+P_{2}\text{e}^{\alpha_{2}z}+P_{3}\text{e}^{\alpha_{3}z}, \end{array}$$where Pj and αi are nonzero constants for j = 1, 2, 3, such that |α1| > |α2| > |α3| and P(z, f, f′, …, f(t) is an algebraic differential polynomial in f(z) of degree no greater than n – 1.

scholarly journals On solutions of some non-linear differential equations in connection to Bruck Conjecture

2017 ◽  
Vol 48 (4) ◽  
pp. 365-375
Author(s):  
Dilip Candra Pamanik ◽  
Manab Biswas
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Entire Solutions ◽  
Linear Complex ◽  
Non Linear ◽  
Complex Differential Equations ◽  
Linear Differential ◽  
Brück Conjecture

In this paper, we investigate on the non-constant entire solutions of some non-linear complex differential equations in connection to Br\"{u}ck conjecture and prove some results which improve and extend the results of Xu and Yang\bf{[Xu HY, Yang LZ. On a conjecture of R. Br\"{u}ck and some linear differential equations. Springer Plus 2015; 4:748,:1-10, DOI 10.1186/s40064-015-1530-5.]}

scholarly journals On transcendental directions of entire solutions of linear differential equations

2021 ◽  
Vol 7 (1) ◽  
pp. 276-287
Author(s):  
Zheng Wang ◽  
◽  
Zhi Gang Huang
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Lower Order ◽  
Difference Operator ◽  
Entire Functions ◽  
Linear Differential Equations ◽  
Entire Solutions ◽  
The Common ◽  
Linear Differential ◽  
Finite Lower Order

<abstract><p>This paper is devoted to studying the transcendental directions of entire solutions of $ f^{(n)}+A_{n-1}f^{(n-1)}+...+A_0f = 0 $, where $ n(\geq 2) $ is an integer and $ A_i(z)(i = 0, 1, ..., n-1) $ are entire functions of finite lower order. With some additional conditions, the set of common transcendental directions of non-trivial solutions, their derivatives and their primitives must have a definite range of measure. Moreover, we obtain the lower bound of the measure of the set defined by the common transcendental directions of Jackson difference operator of non-trivial solutions.</p></abstract>

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