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Oscillation and nonoscillation criteria for second order nonlinear differential equations. I. (English) Zbl 0790.34033
The paper gives sufficient conditions for the oscillation of bounded solutions of the equations $[a(t)g (x(t))x'(t)]'+Q(t) f(x(t))=0$, $[a(t)g(x(t)) x'(t)]'+Q(t) f(x(q(t)))=0$, and the nonoscillation of bounded solutions of the forced equation $[a(t)g(x(t)) x'(t)]'+Q(t) f(x(t))=r(t)$. Some of the conditions assumed in the theorems contain the unknown solution $x(t)$. The paper does not contain actual examples realizing the conditions. In fact, the obtaining of such examples, in my opinion, is too hard. It may be impossible.
Reviewer: A.H.Nasr

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34K99Functional-differential equations
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