Oscillation and nonoscillation criteria are established for the second order linear differential equation [p(t)u'(t)]' + q(t)u(t) = 0, t greater than or equal to t(0), under the hypothesis that p(t) > 0 and integral(infinity) dt/a(t)p(t) < infinity, where a(t) is an element of C-2([t(0),infinity); (0, infinity)) is a given function. These results improve some well-known oscillation and nonoscillation criteria.
