Positive Solutions of Singular Three-Point Boundary Value Problems for the One-Dimensional p-Laplacian

摘要

We use the fixed-point index theory to establish the existence of at least one or two positive solutions for the singular three-point boundary value problems (φ{sub}p(y'))' + a(t) f(y(t)) = 0, 0 < t < 1, y'(0) = 0, y(1) = βy(η), where φ{sub}p(s) = |s|{sup}(p-2)s, p≥2, 0 ≤ β < 1, 0 < η < 1, f ∈ C([0, +∞), [0, +∞)), a ∈ C((0,1), [0, +∞)), and a(t) is allowed to have a singularity at the endpoints of (0,1). Applications of our results are provided to yield positive radial solutions of some partial differential equations boundary value problems on an annulus. As an application, we also give some examples to demonstrate our results.