On the oscillation of second order sublinear ordinary differential equations (Q1374074)

The author presents oscillation results for the second order sublinear ODE \( (r(t)\psi(x)x'(t))' + q(t)g(x(t)) = \phi(t)\) where \(\phi, \psi \in C(\mathbb{R})\) with \( \psi(x) > 0\) for \(x \in \mathbb{R}\), \(xg(x) > 0\) for all \(x \not= 0\) and \(\psi/g\) satisfies the sublinear condition \( \int_{0}^{\mp \varepsilon}\frac{\psi(u)}{g(u)}du < \infty\), for some \(\varepsilon > 0\); \(g\) is differentiable on \(\mathbb{R}\) except possibly at 0 and \(g'(x) > 0\) for all \(x \not= 0\), the functions \( q, r, \phi: [t_0, \infty) \to \mathbb{R}\) with \( r(t) > 0\) for \( t \in [t_0, \infty)\). The results extend and improve results of Kamenev, Kura, Philos and Wong.