Mathematics Commons^™

Positive Solutions For Singular Three-Point Boundary-Value Problems, Ravi P. Agarwal, Donal O'Regan, Baoqiang Yan

Mathematics and System Engineering Faculty Publications

Using the theory of fixed point index, this paper discusses the existence of at least one positive solution and the existence of multiple positive solutions for the singular three-point boundary value problem: y″(t) + a(t)f(t, y(t), y′(t)) = 0, 0 < t < 1, y′(0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, and f may be singular at y = 0 and y′ = 0. .