On existence and multiplicity of positive solutions to singular multi-point boundary value problems

The existence and multiplicity of positive solutions are established for the multi-point boundary value problem −(p(t)u (t )) + F(t,u(t)) = 0, 0 < t <1, u(0) = m j=1 aj u(xj ), w(1) = m j=1 bj w(xj ), where w(t) := p(t)u (t ), aj ,bj ∈ [0,+∞) with 0 < m j=1 aj < 1 and m j=1 bj < 1, xj ∈ (0, 1) with 0 < x1 < x2 < ··· < xm < 1, under certain conditions on p and F. The arguments are based upon the positivity of the Green’s function and the Krasnosel’skii fixed point theorem.  2004 Elsevier Inc. All rights reserved.