Oscillation of a forced second order nonlinear equation (Q1327006)

few oscillation criteria are proved for semilinear differential equations of the type \(x'' + p(t) f(x)= q(t)\), \(t \in I = (t_ 0, \infty)\), where \(p:I \to (0,\infty)\), \(q:I \to \mathbb{R}\) are piecewise continuous, \(q\) is oscillatory at \(\infty\), \(f:\mathbb{R} \to \mathbb{R}\) is continuous and nondecreasing, and \(xf(x)>0\) for all \(x \neq 0\). Unlike most previous work, a geometric approach is employed. The results generalize some previous one of \textit{J. S. W. Wong} [SIAM J. Math. Anal. 19, No. 3, 667- 675 (1988; Zbl 0655.34023)].