On the boundedness of solutions of the equation             $u''+(1+f(t))u=0$

Renato Manfrin

doi:10.3934/dcds.2009.23.991

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2009, Volume 23, Issue 3: 991-1008. Doi: 10.3934/dcds.2009.23.991

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On the boundedness of solutions of the equation $u''+(1+f(t))u=0$

Renato Manfrin^1,

1.
Università IUAV di Venezia, Tolentini, S. Croce 191, 30135 Venezia

Received: January 2008

Revised: August 2008

Published: September 2009

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Abstract

Sufficient conditions on the function $\,f\,$ are given which ensure the boundedness of the solutions of the second order linear differential equation $\,u''+(1+f(t))\,u=0\,$ as $\, t\rightarrow +\infty\,$. To do this, a suitable class of quadratic forms is introduced.

Keywords:

Second order ODE,
boundedness of solutions.

Mathematics Subject Classification: Primary: 34C11; Secondary: 34D10.

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