Geodesic
A note on linear perturbations of oscillatory second order differential equations
Archivum mathematicum, Tome 46 (2010) no. 2, pp. 105-118 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Under suitable hypotheses on $\gamma (t)$, $\lambda (t)$, $q(t)$ we prove some stability results which relate the asymptotic behavior of the solutions of $u^{\prime \prime }+ \gamma (t)u^{\prime }+\big (q(t)+ \lambda (t)\big )u=0$ to the asymptotic behavior of the solutions of $u^{\prime \prime }+ q(t)u=0$.
Under suitable hypotheses on $\gamma (t)$, $\lambda (t)$, $q(t)$ we prove some stability results which relate the asymptotic behavior of the solutions of $u^{\prime \prime }+ \gamma (t)u^{\prime }+\big (q(t)+ \lambda (t)\big )u=0$ to the asymptotic behavior of the solutions of $u^{\prime \prime }+ q(t)u=0$.
Classification : 34C11, 34D10
Keywords: second order ODE; boundedness of solutions; linear perturbations 
@article{ARM_2010_46_2_a3,
     author = {Manfrin, Renato},
     title = {A note on linear perturbations of oscillatory second order differential equations},
     journal = {Archivum mathematicum},
     pages = {105--118},
     year = {2010},
     volume = {46},
     number = {2},
     mrnumber = {2684253},
     zbl = {1240.34186},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010_46_2_a3/}
}
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Manfrin, Renato. A note on linear perturbations of oscillatory second order differential equations. Archivum mathematicum, Tome 46 (2010) no. 2, pp. 105-118. http://geodesic.mathdoc.fr/item/ARM_2010_46_2_a3/