Lower order for meromorphic solutions to linear delay-differential equations
Texas State University, Department of Mathematics
In this article, we study the order of growth for solutions of the non-homogeneous linear delay-differential equation ∑ni=0 ∑mj=0Aijƒ(j) (z + ci) = F(z), where Aij(z) (i = 0,..., n; j = 0,...,m), F(z) are entire or meromorphic functions and ci (0, 1,...,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.
Linear difference equation, Linear delay-differential equation, Meromorphic solution, Order, Type, Lower order, Lower type
Bellaama, R., & Belaïdi, B. (2021). Lower order for meromorphic solutions to linear delay-differential equations. <i>Electronic Journal of Differential Equations, 2021</i>(92), pp. 1-20.