# American Institute of Mathematical Sciences

July  2009, 23(3): 991-1008. doi: 10.3934/dcds.2009.23.991

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

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

Received  January 2008 Revised  August 2008 Published  November 2008

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.
Citation: Renato Manfrin. On the boundedness of solutions of the equation $u''+(1+f(t))u=0$. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 991-1008. doi: 10.3934/dcds.2009.23.991
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