Nonlinear differential polynomials sharing a small function

summary:Dealing with a question of Lahiri [6] we study the uniqueness problem of meromorphic functions concerning two nonlinear differential polynomials sharing a small function. Our results will not only improve and supplement the results of Lin-Yi [16], Lahiri Sarkar [12] but also improve and supplement a very recent result of the first author [1]

Uniqueness and value distribution of differences of entire functions

AbstractWe consider the existence of transcendental entire solutions of certain type of non-linear difference equations. As an application, we investigate the value distribution of difference polynomials of entire functions. In particular, we are interested in the existence of zeros of fn(z)(λfm(z+c)+μfm(z))−a, where f is an entire function, n, m are two integers such that n⩾m>0, and λ, μ are non-zero complex numbers. We also obtain a uniqueness result in the case where shifts of two entire functions share a small function

Normal Families and Complex Dynamics

The schedule comprised more than 25 ordinary and problem session talks from a broad range of areas in function theory, including but not limited to: Nevanlinna theory, iteration of rational functions, dynamics of transcendental entire and meromorphic functions, function algebras, Riemann surfaces, each of them in close connection to the main topic Normal Families and Complex Dynamics

Existence of entire solutions of nonlinear difference equations

summary:In this paper we obtain that there are no transcendental entire solutions with finite order of some nonlinear difference equations of different forms

Generalizations on the results of Cao and Zhang

summary:We establish some uniqueness results for meromorphic functions when two nonlinear differential polynomials $P(f)\prod _{i=1}^{k}(f^{(i)})^{n_{i}}$ and $P(g)\prod _{i=1}^{k}(g^{(i)})^{n_{i}}$ share a nonzero polynomial with certain degree and our results improve and generalize some recent results in Y.-H. Cao, X.-B. Zhang (2012). Also we exhibit two examples to show that the conditions used in the results are sharp

Non-linear differential polynomials sharing one or two values with finite weight

The purpose of the paper is to study the uniqueness of meromorphic functions sharing a small function with finite weight. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [21]. We also solve an open problem as posed in the last section of [21]