Two-point oscillation for a class of second-order damped linear differential equations (Q642706)

Summary: Using the comparison theorem, the two-point oscillation for linear differential equation with damping term \[ y'' + (f(x)/(x - x^2)^\alpha)y' + (g(x)/(x - x^2)^\beta)y = 0 \] is considered, where \(\alpha, \beta > 0\); \(f(x), g(x) > 0\), and \(f, g \in C((0, 1))\). It is shown that \(0 < \alpha < 3/2\), \(\beta > 3\) or \(\alpha > 3/2\), \(\beta > 2\alpha\) imply the two-point oscillation of the equation.