Multi-point boundary value problems on an unbounded domain at resonance

We consider the second-order nonlinear differential equation (p(t)u'(t))' = f(t, u(t), u'(t)), a.e. in (0, infinity), satisfying two sets of boundary conditions: u'(0) = 0, Sigma(n)(i=1) kappa(i) u(T-i) = lim(t ->infinity) u(t) and u(0) = 0, Sigma(n)(i=1) kappa(i) u(T-i) = lim(t ->infinity) u(t), where n >= 1, f : [0, infinity) x R-2 -> R is Caratheodory with respect to L-1[0, infinity). The parameters in the multi-point boundary conditions are such that the corresponding differential operator is non-invertible but nevertheless is a Fredholm map of index zero. As a result the coincidence degree theory can be applied to establish existence theorems. (C) 2008 Published by Elsevier Ltd.