On certain non-linear differential monomial sharing non-zero polynomial

UDC 517.5 With the idea of normal family we study the uniqueness of meromorphic functions and when and share two values, where and is a polynomial. The obtained result significantly improves and generalizes the result in [A. Banerjee, S. Majumder, <em>On certain non-linear differential polynomial sharing a non-zero polynomial</em>, Bol. Soc. Mat. Mex. (2016),https://doi.org/10.1007/s40590-016-0156-0].

An entire function sharing fixed points with its linear differential polynomial

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

AN ENTIRE FUNCTION SHARING TWO VALUES WITH ITS LINEAR DIFFERENTIAL POLYNOMIAL

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].

On meromorphic solutions of certain nonlinear differential equations

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.