Groupes d’automorphismes de et équations différentielles
We investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Our results extend the previous results due to Peng and Chen.
In this paper, we investigate the problem of stability of linear time-varying singular systems, which are transferable into a standard canonical form. Sufficient conditions on exponential stability and practical exponential stability of solutions of linear perturbed singular systems are obtained based on generalized Gronwall inequalities and Lyapunov techniques. Moreover, we study the problem of stability and stabilization for some classes of singular systems. Finally, we present a numerical example...
We show that the growth rates of solutions of the abstract differential equations ẋ(t) = Ax(t), , and the difference equation are closely related. Assuming that A generates an exponentially stable semigroup, we show that on a general Banach space the lowest growth rate of the semigroup is O(∜t), and for it is O(∜n). The similarity in growth holds for all Banach spaces. In particular, for Hilbert spaces the best estimates are O(log(t)) and O(log(n)), respectively. Furthermore, we give conditions...
The main purpose of this paper is to partly answer a question of L. Z. Yang [Israel J. Math. 147 (2005), 359-370] by proving that every entire solution f of the differential equation has infinite order and its hyperorder is a positive integer or infinity, where P is a nonconstant entire function of order less than 1/2. As an application, we obtain a uniqueness theorem for entire functions related to a conjecture of Brück [Results Math. 30 (1996), 21-24].