Lower order for meromorphic solutions to linear delay-differential equations

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. For more information see https://ejde.math.txstate.edu/Volumes/2021/92/abstr.html