Abstract :
This paper investigates the existence of nontrivial solution for the three-point boundary value
problem
u + f (t,u) = 0, 0 < t <1,
u (0) = 0, u(1) = αu(η),
where η ∈ (0, 1), α ∈ R, α = 1, f ∈ C([0, 1] × R,R). Under certain growth conditions on the nonlinearity
f , several sufficient conditions for the existence of nontrivial solution are obtained by using
Leray–Schauder nonlinear alternative. As an application, some examples to demonstrate our results
are given.
2004 Elsevier Inc. All rights reserved
Keywords :
Second-order nonlinear ordinary differential equation , Three-point boundary value problem , Leray–Schauder nonlinear alternative
