Abstract :
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.
