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Graef, John R.; Spikes, Paul W.

On the oscillatory behavior of solutions of second order nonlinear differential equations. (English) Zbl 0627.34034

Czech. Math. J. 36(111), 275-284 (1986).
The authors study the behavior of solutions to \[ (a(t)\psi (t)x')'+q(t)f(t)=r(t) \] where a,\(\psi\),q,f,r are continuous functions, \(a\cdot \psi >0\) for \(x\neq 0\), \(x\cdot f(x)>0\) for \(x\neq 0\), and r is of bounded variation. The authors pay special attention to the case that q(t) changes the sign and give three sets of sufficient conditions for any solution to be either oscillatory or to satisfy \(\liminf | x(t)| =0\) for \(t\to \infty\). The relevant literature and some examples are listed.
Reviewer: E.Brommundt

Cited in 10 Documents

MSC:

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

Keywords:

second order differential equation; examples
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\textit{J. R. Graef} and \textit{P. W. Spikes}, Czech. Math. J. 36(111), 275--284 (1986; Zbl 0627.34034)
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References:

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