Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 92, pp. 1-20.

Title: Lower order for meromorphic solutions to linear delay-differential equations
       
Authors: Rachid Bellaama   (Univ. of Mostaganem, Algeria)
         Benharrat Belaidi (Univ. of Mostaganem, Algeria)

Abstract:
In this article, we study the order of growth for solutions of
the non-homogeneous linear delay-differential equation
$$
\sum_{i=0}^n\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_i)=F(z),
$$
where $A_{ij}(z)$ $(i=0,\dots ,n;j=0,\dots ,m)$,
$F(z)$ are entire or meromorphic functions and $c_i$
$(0,1,\dots ,n) $ are non-zero distinct complex numbers. Under the
condition that there exists one coefficient having the maximal
lower order, or having the maximal lower type, strictly greater than
the order, or the type, of the other coefficients,
we obtain estimates of the lower bound of the order of meromorphic solutions
of the above equation.


Submitted June 25, 2021. Published November 18, 2021.
Math Subject Classifications: 30D35, 39B32, 39A10.
Key Words: Linear difference equation; linear delay-differential equation;
           meromorphic solution; order; type; lower order, lower type.