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Oscillation criteria for half-linear second order differential equations. (English) Zbl 0872.34018

Some oscillation criteria are given for the second order nonlinear differential equation \[ [\Phi(u'(t))]'+ c(t)\Phi(u(t))=0, \] where \(c(t)\) is a continuous function on \([0,\infty)\) and \(\Phi:\mathbb{R}\to\mathbb{R}\) is defined by \(\Phi(x)=|x|^{p-2}x\) with \(p>1\) a fixed real number. If \(p=2\), then these results improve earlier oscillation criteria of Wintner, Hartman, Kamenev and Philos.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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