On oscillation of second-order ''sublinear'' differential equations (Q795209)

Consider the differential equation (*) \(x''(t)+t^{\lambda}p(t)f(x)=0\), \(t\in [0,\infty)\). The authors prove that if 0\(\not\equiv p(t)\in C[0,\infty)\) is periodic, with period w, such that \(\int^{w}_{0}p(t)dt\geq 0,\) and f(x) is an odd function such that \(x^{-\alpha}f(x)\) is nondecreasing in \((0,\infty)\) and \(x^{- \beta}f(x)\) is nonincreasing in \((0,\infty)\) for some constants \(\alpha\),\(\beta\) with \(0<\alpha \leq \beta<1\), then the continuable solutions of (*) are oscillatory for \(0<\lambda<1\).