Abstract :
The existence, nonexistence, and multiplicity of nonnegative solutions are established for the
three-point boundary value problem
−u (t ) = p(t)f (u(t)), 0 < t <1,
u(0) = 0, u(1) −αu(β) = λ,
where β ∈ (0, 1), α ∈ (0, 1/β), and λ is a nonnegative parameter, under appropriate hypotheses. The
key idea is that the problem of finding a nonnegative solution is transformed into the problem of
finding a fixed point of a completely continuous operator. The arguments involve the Schauder fixed
point, the method of upper and lower solutions for three-point boundary value problems and the
Leray–Schauder degree theory.
2003 Elsevier Inc. All rights reserved.
