Oscillation of second-order nonlinear ODE with damping (Q5898311)

The authors consider the differential equation \[ (r(t)k_1(x(t),x'(t)))'+p(t)k_2(x(t),x'(t))x'(t)+ q(t)f(x(t))=0,\qquad t\geq t_0,\tag{1} \] where \(t_0\) is a fixed real number, \(r\in C([t_0,+\infty);(0,+\infty))\), \(p,q\in C([t_0,+\infty);\mathbb R)\), \(f\in C(\mathbb R;\mathbb R)\), and \(k_1,k_2\in C(\mathbb R^2;\mathbb R)\). Conditions are established guaranteeing that \((1)\) is oscillatory.