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

• Autorzy: Ting-Bin Cao , Zhong-Shu Deng
• Języki publikacji: EN

Abstrakty

EN

The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation
$f^{(k)} + a_{k-1}(z)f^{(k-1)} + ⋯ + a₁(z)f' + a₀(z)f = F(z)$,
where all coefficients $a₀,a₁,...,a_{k-1}$, F ≢ 0 are analytic functions in the unit disc 𝔻 = {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.

Kategorie tematyczne

• 34M10: Oscillation, growth of solutions
• 30D35: Distribution of values, Nevanlinna theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2010
• Tom: 97
• Numer: 1
• Strony: 51-61

Daty

wydano

2010

Twórcy

autor

Ting-Bin Cao

• Department of Mathematics, Nanchang University, Nanchang 330031, China

autor

Zhong-Shu Deng

• Editorial office of Journal, Nanchang University, Nanchang 330047, China

Identyfikatory

DOI

10.4064/ap97-1-4