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On oscillatory and asymptotic properties of solutions of certain nonlinear third order differential equations. (English) Zbl 0945.34021
The authors investigate oscillatory and asymptotic properties of solutions to the third-order nonlinear differential equation $x'''+p(t,x,x',x'')x''+q(t,x,x',x'')x'+r(t,x,x',x'')x=f(t,x,x',x''), \tag{*}$ where $$p,q,r,f$$ are continuous functions on $$(\alpha,\infty)\times \mathbb{R}^n$$, $$\alpha\in \mathbb{R}$$. Using the linearization technique combined with a comparison principle conditions on the functions $$p,q,r,f$$ are given which guarantee that every solution to (*) with one zero is oscillatory. Asymptotic properties of nonoscillatory solutions are studied, too.

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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##### References:
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