scholarly journals Meromorphic function sharing a small function with a linear differential polynomial

2016 ◽  
Vol 141 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Indrajit Lahiri ◽  
Amit Sarkar
Keyword(s):  
Meromorphic Function ◽  
Differential Polynomial ◽  
Small Function ◽  
Linear Differential Polynomial ◽  
Linear Differential ◽  
Function Sharing

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.

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].

Meromorphic function sharing a small function with a homogeneous differential polynomial

2019 ◽  
Vol 10 (3) ◽  
pp. 183-192
Author(s):  
Indrajit Lahiri ◽  
Bipul Pal
Keyword(s):  
Meromorphic Function ◽  
Differential Polynomial ◽  
Small Function ◽  
Type Result ◽  
Function Sharing

Abstract In this paper, we consider a Brück-type result for a homogeneous differential polynomial generated by a meromorphic function.

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.

Uniqueness of meromorphic functions of differential polynomials sharing a small function with finite weight

2019 ◽  
Vol 25 (2) ◽  
pp. 141-153
Author(s):  
Harina P. Waghamore ◽  
Vijaylaxmi Bhoosnurmath
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Differential Polynomial ◽  
Small Function ◽  
Differential Polynomials ◽  
Weighted Sharing ◽  
Linear Differential Polynomials ◽  
Linear Differential

Abstract Let f be a non-constant meromorphic function and {a=a(z)} ( {\not\equiv 0,\infty} ) a small function of f. Here, we obtain results similar to the results due to Indrajit Lahiri and Bipul Pal [Uniqueness of meromorphic functions with their homogeneous and linear differential polynomials sharing a small function, Bull. Korean Math. Soc. 54 2017, 3, 825–838] for a more general differential polynomial by introducing the concept of weighted sharing.

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.

scholarly journals Bruck conjecture and certain solution of some differential equation.

2020 ◽  
Vol 51 (3) ◽  
pp. 245-259
Author(s):  
Molla Basir Ahamed
Keyword(s):  
Differential Equation ◽  
Meromorphic Function ◽  
Differential Polynomial ◽  
Small Function ◽  
Brück Conjecture

We investigate on the famous Br$ \ddot{u} $ck conjecture further, and improved some of the existing results by extending them up to a differential monomial $ M[f] $ sharing small function with certain power of $ f^{d_M} $ of a meromorphic function. We have found the class of the meromorphic function satisfying the relation $ f^{d_M}\equiv M[f] $. For the generalizing our main results further up to a differential polynomial $ P[f] $, some relevant  questions finally have been posed for further study in this direction.

Sign in / Sign up

Export Citation Format

Share Document