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On nonoscillatory solutions of a class of nonlinear differential equations. (English) Zbl 0604.34020
Let the quasi-derivatives of y be defined by \(L_ 0y=a_ 0(t)y\), \(L_ iy=a_ i(t)(L_{i-1}y)'\), \(a_ i\), \(i=1,...,n\) are positive continuous functions on [a,\(\infty)\) such that \(\int^{\infty}_{a}a_ i^{- 1}(t)dt=\infty.\) The equation \(L_ ny+(-1)^ nf(t,y,y',...,y^{(m)})=0,\) \(m\in \{0,1,...,n-1\}\) and \(L_ ny\) is the quasi-derivative of y of order n is studied. It is established that every nonoscillatory solution of the problem belongs to a set defined before. Existence was studied in a previously published work.
Reviewer: W.Ames

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34A99 General theory for ordinary differential equations
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