This paper is devoted to studying the transcendental directions of entire solutions of $f^{(n)}+A_{n-1}{f}^{(n-1)}+...+A_{0}f=0$, where $n(\ge 2)$ is an integer and $A_i(z)(i=0,1,...,n-1)$ are entire functions of finite lower order. With some additional conditions, the set of common transcendental directions of non-trivial solutions, their derivatives and their primitives must have a definite range of measure. Moreover, we obtain the lower bound of the measure of the set defined by the common transcendental directions of Jackson difference operator of non-trivial solutions.

This paper is devoted to studying the growth of solutions of $f^{″}+A(z)f^{\prime }+B(z)f=0$, where $A(z)$ and $B(z)$ are meromorphic functions. With some additional conditions, we show that every non-trivial solution $f$ of the above equation has infinite order. In addition, we also obtain the lower bound of measure of the angular domain, in which the radial order of $f$ is infinite.

In this paper, we mainly investigate the radial distribution of Julia sets of difference operators of entire solutions of complex differential equation $F(z)f^n(z)+P(z,f)=0$, where $F(z)$ is a transcendental entire function and $P(z,f)$ is a differential polynomial in $f$ and its derivatives. We obtain that the set of common limiting directions of Julia sets of non-trivial entire solutions, their shifts have a definite range of measure. Moreover, an estimate of lower bound of measure of the set of limiting directions of Jackson difference operators of non-trivial entire solutions is given.