Higher order nonlocal boundary value problems at resonance on the half-line

This paper investigates the solvability of a class of higher order nonlocal boundary value problems of the form u((n))(t) = g(t, u(t), u'(t) ... u((n-1))(t)), a.e. t is an element of (0,infinity) subject to the boundary conditions u((n-1))(0) =( )(n-1)!/xi(n-1)u(xi), u((i))(0) = 0,i = 1, 2, ..., n-2, u((n-1))(infinity) = integral(epsilon )(0)u((n-1))(s)dA(s) where xi > 0, g : [0, infinity) x R-n -> R Th is a Caratheodory's function, A : [0,xi] -> [0,1) is a non-decreasing function with A(0) = 0, A(xi) = 1. The differential operator is a Fredholm map of index zero and non-invertible. We shall employ coicidence degree arguments and construct suitable operators to establish existence of solutions for the above higher order nonlocal boundary value problems at resonance.