Related papers: On Picard Value Problem of Some Difference Polynom…
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a…
We shall give bounds on the spacing of zeros of certain functions belonging to the Laguerre-Polya class and satisfying a second order differential equation. As a corollary we establish new sharp inequalities on the extreme zeros of the…
Zeros of many ensembles of polynomials with random coefficients are asymptotically equidistributed near the unit circumference. We give quantitative estimates for such equidistribution in terms of the expected discrepancy and expected…
In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.
We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…
We study Picard's exceptional values of holomorphic one-parametric families of entire functions. Our first result shows that the set of parameter values for which zero is a Picard value can be an arbitrary closed set of zero logarithmic…
We study the probability distribution of the number of common zeros of a system of $m$ random $n$-variate polynomials over a finite commutative ring $R$. We compute the expected number of common zeros of a system of polynomials over $R$.…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
Our aim in this paper is to prove, under some growth conditions on the datas, the solvability in a Gevrey class of a polynomially nonlinear functional differential equation.
For distributions, we build a theory of higher order pointwise differentiability comprising, for order zero, {\L}ojasiewicz's notion of point value. Results include Borel regularity of differentials, higher order rectifiability of the…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
I begin from a particular field of generalised Puiseux series and investigate a class of nonlinear differential equations in the field. It is appeared that the main part of differential equation determines solvability and positions of…
Nevanlinna's second main theorem is a far-reaching generalisation of Picard's Theorem concerning the value distribution of an arbitrary meromorphic function f. The theorem takes the form of an inequality containing a ramification term in…
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
Let $\mathfrak{f}$ be a transcendental entire function with hyper-order less than one. The aim of this note is to study the value distribution of the differential-difference monomials $\alpha \mathfrak{f}(z)^{q_0}(\mathfrak{f}(z+c))^{q_1}$,…
The purpose of the present paper is to examine the zeros of $R$-Bonacci polynomials and their derivatives. We confirm a conjecture about the zeros of $R$-Bonacci polynomials for some special cases. We also find explicit formulas of the…
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
In the paper, we investigate the uniqueness problem of entire functions concerning their linear differential polynomial in shift and obtain three results which improve and generalize the recent result due to Qi (Ann. Polon. Math., 102…