This paper investigates the solvability of a class of higher order nonlocal boundaryvalue problems of the formu(n)(t) = g(t, u(t), u0(t)· · · u(n−1)(t)), a.e. t ∈ (0, ∞)subject to the boundary conditionsu(n−1)(0) = (n − 1)!ξn−1u(ξ), u(i)(0) = 0, i = 1, 2, . . . , n − 2,u(n−1)(∞) = Z ξ0u(n−1)(s)dA(s)where ξ > 0, g : [0, ∞) × <n −→ < is a Caratheodory’s function,A : [0, ξ] −→ [0, 1) is a non-decreasing function with A(0) = 0, A(ξ) = 1. The differential operatoris a Fredholm map of index zero and non-invertible. We shall employ coicidence degree argumentsand construct suitable operators to establish existence of solutions for the above higher ordernonlocal boundary value problems at resonance.
Positive solutions of some higher order nonlocal boundary value problems
