Growth of solutions to two systems of q-difference differential equations

Abstract

This paper is devoted to studying the growth of entire or meromorphic solutions to two systems of q-difference differential equations. The estimates on the growth order of meromorphic solutions are obtained, which are extensions of previous results due to Xu et al. Examples are given to illustrate the existence of solutions of such systems.

Gevrey versus q−Gevrey Asymptotic Expansions for Some Linear q−Difference-Differential Cauchy Problem

“…This is the case of the recent works by H. Tahara [14], H. Yamazawa [18] and H. Tahara and H. Yamazawa [15]; the authors and J. Sanz [8] and with T. Dreyfus [3]. A different approach via Nevalinna theory is developped in [16,17]. The importance of applications of q-difference equations in the knowledge of wavelets or tsunami and rogue waves is evidenced in recent advances in the field such as [12,13].…”