Complex oscillation of differential polynomials in the unit disc
✍ Scribed by Latreuch, Zinelaâbidine; Belaïdi, Benharrat; Farissi, Abdallah
- Book ID
- 120017478
- Publisher
- Springer Netherlands
- Year
- 2013
- Tongue
- English
- Weight
- 200 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0031-5303
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## Abstract In this paper, we investigate the complex oscillation theory of the second order linear differential equation __f__ ″ + __A__ (__z__)__f__ = 0, where the coefficient __A__ (__z__) is an analytic function in the unit disc Δ = {__z__: |__z__ | < 1} (© 2009 WILEY‐VCH Verlag GmbH & Co. K
Let f , f be two linearly independent solutions of the linear differential 1 2 ## Ž . Ž . equation f Љ q A z f s 0, where A z is transcendental entire, and assume that the exponents of convergence for the zero-sequences of f , f satisfy 1 2 Ž Ž . Ž .. max f , f s ϱ. Our main result proves that th
We treat the linear differential equation ) f q A z f s 0, where k P 2 is Ž . Ž . an integer and A z is a transcendental entire function of order A . It is shown Ž . Ž . Ž . Ž . that any non-trivial solution of the equation ) satisfies f P A , where f is the exponent of convergence of the zero-sequ