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Oscillation criteria for second order nonlinear differential equations involving general means. (English) Zbl 0964.34028

New oscillation criteria for \[ y''+ a(t) f(y)= 0\tag{\(*\)} \] are obtained, with \(a\in C([0, \infty),\mathbb{R})\), \(f\in C^1(\mathbb{R}, \mathbb{R})\), \(f'(y)\geq 0\) and \(yf(y)> 0\) for \(y\neq 0\). Moreover, \(f(y)\) satisfies either a superlinear or a sublinear condition and \(a(t)\) is allowed to change sign. Kamenev-type oscillation criteria involving integral averages for \(y''+ a(t)y=0\) are extended to \((*)\) by using more general means. The present work generalizes many other earlier works.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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