CONJUGACY CRITERIA FOR 2ND-ORDER DIFFERENTIAL-EQUATIONS

Oscillation properties of linear differential equations of the second order (*) (r(x)y')' + p(x)y = 0, x is-an-element-of = (a, b), -infinity less-than-or-equal-to a < b less-than-or-equal-to infinity, are viewed as a perturbation of the disconjugate equation (**) (r(x)y')' = 0. Sufficient conditions on the coefficients r(x),p(x) ensuring that (*) possesses a nontrivial solution having at least two zeros on I are obtained. It is shown that conjugacy criteria for (*) are different in the case where the principal solutions y(a), y(b) of (**) at a and b are linearly independent or linearly dependent.