Fast growth and fixed points of solutions of higher-order linear differential equations in the unit disc

• Published in: AIMS mathematics Vol. 6; no. 10; pp. 10833 - 10845
• Main Authors: Chen, Yu, Deng, Guantie
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: characteristic function; fixed points; iterated order; linear differential equations; unit disc
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021629

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.