(untitled) (European Journal of Pure and Applied Mathematics, 2020)
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(0,∞) subject to the boundary conditions eqnarray* u^(n-1)(0) &=& (n-1)!ξ^n-1 u(ξ), u^(i)(0) = 0, i=1,2,…, n-2, u^(n-1)(∞) &=& ^ξ_0 u^(n-1)(s)dA(s) eqnarray* 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 operator is a Fredholm map of index zero and non-invertible. We shall employ coincidence degree arguments and construct suitable operators to establish existence of solutions for the above higher order nonlocal boundary value problems at resonance.