Some remarks about the nonoscillatory solutions. (English) Zbl 1090.34532

Švec, Marko; Hricišáková, Daniela

Arch. Math., Brno 36, Suppl., 617-622 (2000).

In the paper nonoscillatory properties of (1) \(z^{(4)} + p(x) z = f(x)\) are studied where \(p\geq 0\) and \(f\) is one-sided function in a neighbourhood of the infinity. If \(y^{(4)} + p(x) y = 0\) is nonoscillatory and \(p\) and \(f\) are not identically zero on a subinterval then (1) is nonoscillatory, too. Note, that the correct form of (2) in the paper is the equation (1) given above.

Reviewer: Miroslav Bartušek (Brno)

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

nonoscillatory solutions; homogeneous differential equation; nonhomogeneous differential equation