Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

On non-normal solutions of linear differential equations


Author: Janne Gröhn
Journal: Proc. Amer. Math. Soc. 145 (2017), 1209-1220
MSC (2010): Primary 34C10
DOI: https://doi.org/10.1090/proc/13292
Published electronically: September 8, 2016
MathSciNet review: 3589320
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Normality arguments are applied to study the oscillation of solutions of $ f''+Af=0$, where the coefficient $ A$ is analytic in the unit disc $ \mathbb{D}$ and $ \sup _{z\in \mathbb{D}} (1-\vert z\vert^2)^2\vert A(z)\vert < \infty $. It is shown that such a differential equation may admit a non-normal solution having prescribed uniformly separated zeros.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 34C10

Retrieve articles in all journals with MSC (2010): 34C10


Additional Information

Janne Gröhn
Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
Email: janne.grohn@uef.fi

DOI: https://doi.org/10.1090/proc/13292
Keywords: Linear differential equation, normal function, oscillation theory, prescribed zeros, separation of zeros
Received by editor(s): February 2, 2016
Received by editor(s) in revised form: May 13, 2016
Published electronically: September 8, 2016
Additional Notes: The author was supported in part by the Academy of Finland, projects #258125 and #286877.
Communicated by: Stephen Ramon Garcia
Article copyright: © Copyright 2016 American Mathematical Society