Nonresonant nonlinear singular problems in the limit circle case

Existence results are presented for the "nonresonant" singular boundary value problem (1/p)(py')' + μqy = f(t, y) a.e. on [0, 1] with lim_t→0+ p(t)y'(t) = y(1) = 0. Here we do not assume ∫¹₀(ds/p(s)) < ∞ but only that ∫¹₀(1/p(s))(∫^s₀ p(x)q(x) dx)^1/2 ds < ∞. As a result the appropriate eigenvalue problem will have a regular endpoint at t = 1 and a singular endpoint of limit circle type at t = 0.