Positive solutions of three-point boundary value problems for the one-dimensional p-laplacian with infinitely many singularities

AbstractWe consider thesingular three-point boundary value problems (φp(y′))′ + a(t)f(y(t)) = 0, 0 < t < 1, y′(0) = 0, y(1) = βy(ƞ), where φp(s) = |s|p−2s, p ≥ 2, 0 < β < 1, 0 < η < 1, f ϵ C([0, + ∞), [0, + ∞)), a: [0,1] → [0, + ∞), andhas countably many singularities in [0, frsol|1/2). We show that there exist countably many positive solutions by using the fixed-point index theory