Abstract
This paper concerns the oscillation of solutions to the differential equation
(r(t)x'(t))' + p(t)x'(t) + q(t)g(x(t)) = 0,
where xg(x) > 0 for all x not equal 0, r(t) > 0 for t >= t(0) > 0. No sign conditions are imposed on p(t) and q(t). Our results solve the open problem posed by Rogovchenko [27], complement the results in Sun [29], and improve a number of existing oscillation criteria. Our main results are illustrated with examples.