Oscillation of meromorphic solutions to linear differential equations with coefficients of [p,q]-order

Abstract

We study the relationship between "small functions" and the derivative of solutions to the higher order linear differential equation $$ f^{(k)}+A_{k-1}f^{(k-1)}+\dots+A_0f=0,\quad (k\geq 2) $$ Here $A_j(z)\; (j=0,1,\dots,k-1)$ are entire functions or meromorphic functions of [p,q]-order.

Keywords

• Linear differential equation
• oscillation
• small function
• [p,q]-order