Certain nonlinear differential polynomial sharing a nonzero polynomial IM

Uniqueness Results for a Nonlinear Differential Polynomial

In this paper, we study a uniqueness question of meromorphic functions whose nonlinear differential polynomials share a nonzero small function. The results in this paper improve and extend many known results. 2010 Mathematics Subject Classification: 30D35, 30D30

ON THE EDGE COVER POLYNOMIAL OF CERTAIN GRAPHS

Let $G$ be a simple graph of order $n$ and size $m$.The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$,where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we stud...

Differential Polynomial Rings of Triangular Matrix Rings

Uniqueness and Differential Polynomials of Meromorphic Functions Sharing a Polynomial

In this paper, we deal with the uniqueness problems of meromorphic functions when certain nonlinear differential polynomials generated by them share a nonconstant polynomial counting multiplicities by considering that the functions share in nity, ignoring multiplicities. The research ndings also include IM-analogues of the theorem in which the nonconstant polynomial is allowed to be shared igno...

Polynomial solutions of certain differential equations arising in physics

Conditions for the existence of polynomial solutions of certain second-order differential equations have recently been investigated by several authors. In this paper a new algorithmic procedure is given to determine necessary and sufficient conditions for a differential equation with polynomial coefficients containing parameters to admit polynomial solutions and to compute these solutions. The ...