scholarly journals When an entire function and its linear differential polynomial share two values

2000 ◽  
Vol 44 (2) ◽  
pp. 349-362 ◽  
Author(s):  
Ping Li ◽  
Chung-Chun Yang
Keyword(s):  
Entire Function ◽  
Differential Polynomial ◽  
Linear Differential Polynomial ◽  
Linear Differential

scholarly journals On entire solutions of a certain type of nonlinear differential equation

2001 ◽  
Vol 64 (3) ◽  
pp. 377-380 ◽  
Author(s):  
Chung-Chun Yang
Keyword(s):  
Differential Equation ◽  
Entire Function ◽  
Finite Order ◽  
Nonlinear Differential Equation ◽  
Entire Solution ◽  
Differential Polynomial ◽  
Entire Solutions ◽  
Value Distribution Theory ◽  
Linear Differential Polynomial ◽  
Linear Differential

In this note, we shall study, via Nevanlinna's value distribution theory, the uniqueness of transcendental entire solutions of the following type of nonlinear differential equation: (*) L (f (z)) – p (z) fn(z) = h (z), where L (f) denotes a linear differential polynomial in f with polynomials as its co-efficients, p (z) a polynomial (≢ 0), h an entire function, and n an integer ≥ 3. We show that if the equation (*) has a finite order transcendental entire solution, then it must be unique, unless L (f) ≡ 0.

AN ENTIRE FUNCTION SHARING TWO VALUES WITH ITS LINEAR DIFFERENTIAL POLYNOMIAL

2017 ◽  
Vol 97 (2) ◽  
pp. 265-273
Author(s):  
INDRAJIT LAHIRI
Keyword(s):  
Entire Function ◽  
Differential Polynomial ◽  
Value Sharing ◽  
Linear Differential Polynomial ◽  
Linear Differential ◽  
Function Sharing

We consider the uniqueness of an entire function and a linear differential polynomial generated by it. One of our results improves a result of Li and Yang [‘Value sharing of an entire function and its derivatives’, J. Math. Soc. Japan51(4) (1999), 781–799].

scholarly journals An entire function sharing fixed points with its linear differential polynomial

2018 ◽  
Vol 22 (1) ◽  
pp. 125-136
Author(s):  
Imrul Kaish ◽  
Indrajit Lahiri
Keyword(s):  
Entire Function ◽  
Fixed Points ◽  
Entire Functions ◽  
Differential Polynomial ◽  
Differential Polynomials ◽  
Linear Polynomial ◽  
Linear Differential Polynomial ◽  
Linear Differential Polynomials ◽  
Linear Differential ◽  
Function Sharing

We study the uniqueness of entire functions, when they share a linear polynomial, in particular, fixed points, with their linear differential polynomials.

scholarly journals On meromorphic solutions of certain nonlinear differential equations

2002 ◽  
Vol 66 (2) ◽  
pp. 331-343 ◽  
Author(s):  
J. Heittokangas ◽  
R. Korhonen ◽  
I. Laine
Keyword(s):  
Meromorphic Function ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Differential Polynomial ◽  
Meromorphic Solutions ◽  
Linear Differential Polynomial ◽  
Linear Differential

In this paper, we consider the growth of meromorphic solutions of nonlinear differential equations of the form L (f) + P (z, f) = h (z), where L (f) denotes a linear differential polynomial in f, P (z, f) is a polynomial in f, both with small meromorphic coefficients, and h (z) is a meromorphic function. Specialising to L (f) − p (z) fn = h (z), where p (z) is a small meromorphic function, we consider the uniqueness of meromorphic solutions with few poles only. Our results complement earlier ones due to C.-C. Yang.

Sign in / Sign up

Export Citation Format

Share Document