On nonoscillatory solutions of a class of nonlinear differential equations. (English) Zbl 0604.34020

Mikunda, Ján; Rovder, Jozef

Math. Slovaca 36, 29-38 (1986).

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

MSC:

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

Keywords:

first order differential equation; quasi-derivatives; nonoscillatory solution

References:

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