Interval criteria for oscillation of second-order linear ordinary differential equations

New oscillation criteria are established for the equation (py')' + qy = 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t(0),infinity), rather than on the whole half-line. Our results are more natural according to the Sturm Separation Theorem and sharper than some previous results, and can be applied to extreme cases such as integral(t0)(infinity)q(t) dt = -infinity. (C) 1999 Academic Press.