Open AccessFast growth and fixed points of solutions of higher-order linear differential equations in the unit disc
Author(s) -
Chen Yu,
Guantie Deng
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021629
Subject(s) - mathematics , iterated function , mathematical analysis , unit (ring theory) , fixed point , differential equation , linear differential equation , convergence (economics) , order (exchange) , exponent , boundary (topology) , linguistics , philosophy , mathematics education , finance , economics , economic growth
In this paper, we investigate the fast growing solutions of higher-order linear differential equations where $ A_0 $, the coefficient of $ f $, dominates other coefficients near a point on the boundary of the unit disc. We improve the previous results of solutions of the equations where the modulus of $ A_{0} $ is dominant near a point on the boundary of the unit disc, and obtain extensive version of iterated order of solutions of the equations where the characteristic function of $ A_{0} $ is dominant near the point. We also obtain a general result of the iterated exponent of convergence of the fixed points of the solutions of higher-order linear differential equations in the unit disc. This work is an extension and an improvement of recent results of Hamouda and Cao.