On limit directions of Julia sets of entire solutions of linear differential equations

This paper is devoted to studying the limit directions of Julia sets of solutions of f(n)+An−1(z)f(n−1)+⋯+A0(z)f=0, where n(≥2) is an integer and Aj(z)(j=0,1,…,n−1) are entire functions of finite lower order. With some additional conditions on coefficients, we know that every non-trivial solution f(z) of such equations has infinite lower order, and prove that the limit directions of Julia sets of f(z) must have a definite range of measure.