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Proceedings of the American Mathematical Society

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

 

 

Unexpected behavior for solutions of a second order, selfadjoint equation


Author: H. Arthur DeKleine
Journal: Proc. Amer. Math. Soc. 33 (1972), 210
MSC: Primary 34C99
DOI: https://doi.org/10.1090/S0002-9939-1972-0293164-7
MathSciNet review: 0293164
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Abstract: Positive, continuous functions $ a(t)$ and $ p(t)$ such that $ a(t)p(t) \equiv t$ and for which some solution of the selfadjoint equation $ (pu')' + au = 0$ satisfies $ \lim \;{\sup _{t \to \infty }}\vert u(t)\vert > 0$ are shown to exist.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293164-7
Keywords: Asymptotic behavior, bounded solutions
Article copyright: © Copyright 1972 American Mathematical Society