Linear Perturbations of a Nonoscillatory Second Order Differential Equation Ii
نویسنده
چکیده
Let y1 and y2 be principal and nonprincipal solutions of the nonoscillatory differential equation (r(t)y′)′ + f(t)y = 0. In an earlier paper we showed that if ∫∞(f − g)y1y2 dt converges (perhaps conditionally), and a related improper integral converges absolutely and sufficently rapidly, then the differential equation (r(t)x′)′ + g(t)x = 0 has solutions x1 and x2 that behave asymptotically like y1 and y2. Here we consider the case where ∫∞(f−g)y2 2 dt converges (perhaps conditionally) without any additional assumption requiring absolute convergence.
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