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 ) + A n − 1 ( z ) f ( n − 1 ) + ⋯ + A 0 ( z ) f = 0 , where n ( ≥ 2 ) is an integer and A j ( 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.