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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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