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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.


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

  • [1] A. Meir, D. Willett and J. S. W. Wong, On the asymptotic behavior of solutions of $ x'' + a(t)x = 0$, Michigan Math. J. 14 (1967), 47-52. MR 35 #463. MR 0209566 (35:463)
  • [2] D. Willett, On an example in second order linear ordinary differential equations, Proc. Amer. Math. Soc. 17 (1966), 1263-1266. MR 34 #1612. MR 0201730 (34:1612)

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Additional Information

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

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