Existence of at least three solutions of nonlinear three point boundary value problems with super-quadratic growth

We establish the existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type −x = f (t,x,x ), 0 < t <1, x (0) = 0, x(1) = δx(η), 0<η<1, 0 < δ <1. We employ a condition weaker than the well-known Nagumo condition which allows the nonlinearity f (t,x,x ) to grow faster than quadratically with respect to x in some cases. Our method uses some degree theory arguments. © 2006 Elsevier Inc. All rights reserved