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Criteria of property $$A$$ for third order superlinear differential equations. (English) Zbl 0776.34028
The paper deals with two superlinear differential equations, namely $$y'''+p(t)y'+q(t)| y|^ \alpha\text{sgn} y=0$$ and $$y'''+p(t)y'+q(t)f(y)=0$$, where $$\alpha>1$$ is a quotient of odd positive numbers. Property $$A$$ means that each solution $$u$$ of the related equation is either oscillatory or there exists a point $$T\geq a$$ such that $$(-1)^ ju^{(j)}\text{sgn} u(t)>0$$ for every $$t\geq T$$, $$j=0,1,2$$, and $$\lim_{t\to\infty}u^{(j)}(t)=0$$, $$j=0,1,2$$. Sufficient conditions for property $$A$$ are obtained for both the equations above which extends and improves some related results cited in the references.
Reviewer: J.Andres (Olomouc)

##### MSC:
 34C11 Growth and boundedness of solutions to ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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##### References:
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