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Integral conditions of oscillation of a linear differential equation. (English) Zbl 0685.34029
Differential equations of the form \[ y^{(n)}(t)+p(t)y(t)=0,\quad t\in [1,\infty),\quad n\geq 2,\quad p(t)>0\quad continuous \] are considered. Two sufficient integral conditions are derived which guarantee: if n is even, then every solution y(\(\cdot)\) is oscillatory, i.e. the set of zeros is unbounded; if n is odd, then y(\(\cdot)\) is oscillatory or \(\lim_{t\to \infty}y^{(i)}(t)=0,\) \(i=0,...,n-1\).
Reviewer: A.Ilchmann

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
Full Text: EuDML
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