40 research outputs found
Growth of Solutions of Complex Differential Equations in a Sector of the Unit Disc
In this paper, we deal with the growth of solutions of homogeneous linear
complex differential equation by using the concept of lower
[\textit{p,q}]-order and lower [\textit{p,q}]-type in a sector of the unit disc
instead of the whole unit disc, and we obtain similar results as in the case of
the unit disc.Comment: 21 page
On Picard Value Problem of Some Difference Polynomials
In this paper, we study the value distribution of zeros of certain nonlinear
difference polynomials of entire functions of finite order.Comment: 17 page
Differential polynomials generated by solutions of second order non-homogeneous linear differential equations
This paper is devoted to studying the growth and the oscillation of solutions of the second order non-homogeneous linear differential equation
f′′ + Aea1z f′ + B(z) ea2z f = F(z) ea1z,
where A, a1, a2 are complex numbers, B(z) (≢ 0) and F(z) (≢ 0) are entire functions with order less than one. Moreover, we investigate the growth and the oscillation of some differential polynomials generated by solutions of the above equation
Nonhomogeneous linear differential polynomials generated by solutions of complex differential equations in the unit disc
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Growth of -order solutions of linear differential equations with entire coefficients
The main aim of this paper is to study the growth of solutions of higher
order linear differential equations using the concepts of -order and -type. We obtain some results
which improve and generalize some previous results of Kinnunen \cite{13}, Long
et al. \cite{L} as well as Bela\"{\i}di \cite{b3}, \cite{b5}.Comment: 21 page
Finite Logarithmic Order Meromorphic Solutions of Complex Linear Delay-Differential Equations
In this article, we study the growth of meromorphic solutions of linear
delay-differential equation of the form \begin{equation*}
\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}%
where and are meromorphic of finite logarithmic order, are
distinct non-zero complex constants. We extend those results obtained recently
by Chen and Zheng, Bellaama and Bela\"{\i}di to the logarithmic lower order.Comment: 23 page
GROWTH OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
This paper is devoted to studying the growth of solutions
of the higher order nonhomogeneous linear differential equation
f(k) + Ak−1f(k−1) + ... + A2f
"
+ (D1 (z) + A1 (z) eP(z)) f
'
+ (D0 (z) + A0 (z)e Q(z)) f = F (k ≥ 2) ,
where P (z) , Q(z) are nonconstant polynomials such that deg P =
degQ = n and Aj (z) (j = 0, 1, ..., k − 1) , F (z) are entire functions
with max{p(Aj) (j = 0, 1, ..., k − 1) , p(Dj) (j = 0, 1)} < n. We also
investigate the relationship between small functions and the solutions of
the above equation