On Perturbative Hardy-Type Inequalities

Given a three-coefficient Sturm-Liouville differential expression tau 0 = r-1 0 interval (a, b) subset of R, we employ the existence of a strictly positive solution u0(lambda 0, center dot) > 0 on (a, b) of tau 0u0 = lambda 0u0 to derive a quadratic form inequality for tau q1 that naturally generalizes the well-known Hardy inequality and re-duces to it in the particular case p0 = r0 = u0(0, center dot) = 1, q0 = lambda 0 = 0, a is an element of R, b = infinity. [-(d/dx)p0(d/dx) + q0] and its perturbation tau q1 = tau 0 + r-1 0 q1 on an