Geodesic
Integral Averaging Techniques for Oscillation of Second Order Nonlinear Differentialequations With Damping
Publications de l'Institut Mathématique, _N_S_68 (2000) no. 82, p. 92

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New oscillation criteria are established for the second order nonlinear differential equation with a damping term $ [a(t)\psi(x(t))x'(t)]'+p(t)x'(t)+q(t)f(x(t))=0. $ These criteria are obtained by using an integral averaging technique. Moreover, we give conditions which ensure that every solution $x(t)$ of the forced second order differential equation with a damping term $ [a(t)\psi(x(t))x'(t)]'+p(t)x'(t)+q(t)f(x(t))=r(t) $ satisfies $\liminf_{t\to\infty} |x(t)|=0$.
Classification : 34C10 34C15
Keywords: Oscillation, Nonlinear differential equations, Integral averages 
@article{PIM_2000_N_S_68_82_a10,
     author = {Jelena V. Manojlovi\'c},
     title = {Integral {Averaging} {Techniques} for {Oscillation} of {Second} {Order} {Nonlinear} {Differentialequations} {With} {Damping}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {92 },
     publisher = {mathdoc},
     volume = {_N_S_68},
     number = {82},
     year = {2000},
     zbl = {1012.34032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a10/}
}
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Jelena V. Manojlović. Integral Averaging Techniques for Oscillation of Second Order Nonlinear Differentialequations With Damping. Publications de l'Institut Mathématique, _N_S_68 (2000) no. 82, p. 92 . http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a10/