Research article

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

  • Received: 27 January 2021 Accepted: 12 July 2021 Published: 26 July 2021
  • MSC : 30D35, 34M10

  • 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.

    Citation: Yu Chen, Guantie Deng. Fast growth and fixed points of solutions of higher-order linear differential equations in the unit disc[J]. AIMS Mathematics, 2021, 6(10): 10833-10845. doi: 10.3934/math.2021629

    Related Papers:

  • 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.



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