Yan's oscillation theorem revisited (Q1036830)

The authors study the oscillation of the second order differential equation \[ (r(t)\,x'(t))'+p(t)\,x'(t)+q(t)\,x(t)=0, \quad t\in[t_0,\infty). \] They extend the result by \textit{J.~Yan} [Proc. Am. Math. Soc. 98, 276--282 (1986; Zbl 0622.34027)] by removing one of the assumptions. The authors work out in details one of the examples from the above Yan's paper \[ (t^\lambda\,x'(t))'+t^\mu\,\sin t\,x'(t)+t^3\,\cos t\,x(t)=0, \] to which the original oscillation theorem could not be applied, while the new presented theorem yields the oscillation of this equation for all \(\lambda\in[-1,1)\) and \(\mu\in(-\infty,-1]\).