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Solutions of non-homogeneous linear differential equations in the unit disc

Ting-Bin Cao, Zhong-Shu Deng (2010)

Annales Polonici Mathematici

The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + + a ( z ) f ' + a ( z ) f = F ( z ) , where all coefficients a , a , . . . , a k - 1 , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.

Solutions of Riemann–Weber type half-linear differential equation

Ondřej Došlý (2017)

Archivum Mathematicum

We establish an asymptotic formula for a pair of linearly independent solutions of the subcritical Riemann–Weber type half-linear differential equation. We also complement the results of the author and M. Ünal, Acta Math. Hungar. 120 (2008), 147–163, where the equation was considered in the critical case.

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