Oscillation criteria for second order linear differential equations
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 \textit{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.
scientific article; zbMATH DE number 811231