Oscillation and nonoscillation criteria for second order nonlinear differential equations. I (Q1312721)

The paper gives sufficient conditions for the oscillation of bounded solutions of the equations \([a(t)g (x(t))x'(t)]'+Q(t) f(x(t))=0\), \([a(t)g(x(t)) x'(t)]'+Q(t) f(x(q(t)))=0\), and the nonoscillation of bounded solutions of the forced equation \([a(t)g(x(t)) x'(t)]'+Q(t) f(x(t))=r(t)\). Some of the conditions assumed in the theorems contain the unknown solution \(x(t)\). The paper does not contain actual examples realizing the conditions. In fact, the obtaining of such examples, in my opinion, is too hard. It may be impossible.