Oscillation criteria for second order linear differential equations. (English) Zbl 0836.34033

Li, Horng Jaan

J. Math. Anal. Appl. 194, No. 1, 217-234 (1995).

It is considered the differential equation (1) \(|r(t)x']' + c(t)x = 0\), where \(r \in C^1 ([t_0, \infty)\); \((0, \infty))\), \(c \in C ([t_0, \infty); \mathbb{R})\) and \(t_0 \geq 0\). The author gives new oscillation criteria for (1) which improve results of A. Wintner, P. Hartman, I. V. Kamenev, J. Yan and Ch. G. Philos. The criteria are proved by using a generalized Riccati transformation due to Y. H. Yu [Math. Nachr. 153, 137-143 (1991; Zbl 0795.34025)] of the form \[ v(t) = \exp \Bigl( - 2 \int^t f(s)ds \Bigr) r(t) \left( {x'(t) \over x(t)} + f(t) \right), \] where \(f \in C^1 ([t_0, \infty); \mathbb{R})\) is a given function.

Reviewer: S.Staněk (Olomouc)

MSC:

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

Keywords:

oscillation criteria; generalized Riccati transformation

Citations:

Zbl 0795.34025