Hi,
For a linear complex differential equation f^(k)+A_(k-1) f^(k-1)+...+A_0 f=0, the coefficients A_j are of finite (p,q)-order, I need to know the conditions on the coefficients that make all solutions of the equation above of infinite (p,q)-order.
I need papers, of any references .
Best regards
Hello Mohamed Amine Zemirni,
I hope I could help you, see the following papers :
[1] H. U. I. Hu and X. Zheng, “GROWTH OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH ANALYTIC COEFFICIENTS OF [ p, q ] -ORDER IN THE UNIT DISC,” vol. 2014, no. 204, pp. 1–12, 2014.
[2] G. Zhang and J. Wang, “the Infinite Growth of Solutions of Complex Differential Equations of Which Coefficient With Dynamical Property,” Taiwan. J. Math., vol. 18, no. 4, pp. 1063–1069, 2014.
[3] M.-S. Liu and C.-L. Yuan, “The growth of meromorphic solutions for a class of higher-order linear differential equations,” Appl. Anal., vol. 85, no. 9, pp. 1189–1199, Sep. 2006.
Many Thanks Hamou Maamar Maghnia
These three articles are very useful to estimate the (p+1,q)-order of solutions and prove the infinity of (p,q)-order but in the unit disc, and in particular when p=2, q=1 in complex plane, so, the natural question is about the possibility of generalising these results to arbitrary (p,q)-order where p>=q>1 an in complex plane.
Thanks again,
- Badges
- Science topic
- Similar topics
- Mathematics
- Applied Mathematics
- Differential Equations