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)

 

 

On boundedness of solutions of second order differential equations in the limit circle case


Author: Man Kam Kwong
Journal: Proc. Amer. Math. Soc. 52 (1975), 242-246
MSC: Primary 34B20
DOI: https://doi.org/10.1090/S0002-9939-1975-0387710-5
MathSciNet review: 0387710
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A differential equation of the form $ x''(t) + a(t)x(t) = 0,t \geqslant 0$, is said to be in the limit circle case if all its solutions are square integrable on $ [0,\infty )$. It has been conjectured in [1] that all its solutions are bounded. J. Walter recently gave a counterexample. This paper gives a method of modifying any given equation in the limit circle case with bounded solutions to produce one with unbounded solutions.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B20

Retrieve articles in all journals with MSC: 34B20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0387710-5
Keywords: Limit circle case, unbounded solutions
Article copyright: © Copyright 1975 American Mathematical Society