Abstract. In this paper, the dynamics on a transcendental entire semigroup G is investigated. We show the possible values of any limit function of G in strictly wandering domains and Fatou components, respectively. Moreover, if G is of class B, for any z in a Fatou domain, there does not exist a sequence {g k } of G such that g k (z) → ∞ as k → ∞.

<abstract><p>This paper is devoted to studying the growth of solutions of $ f''+A(z)f'+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.</p></abstract>

<abstract><p>This paper is devoted to studying the transcendental directions of entire solutions of $ f^{(n)}+A_{n-1}f^{(n-1)}+...+A_0f = 0 $, where $ n(\geq 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.</p></abstract>