Higher-order p-Laplacian boundary value problem at resonance on an unbounded domain

In this work, we employ the extension of Mawhin's coincidence degree by Ge and Ren to investigate the solvability of the p-Laplacian higher-order boundary value problems of the form (w(t)phi(p)(x((n-1))(t)))' = h(t, x(t), ..., x((n-1))(t)), 0 < t < infinity, x((n-2))(0) = (n-2)!/eta(n-2)x(eta), x((n-1))(0) = x((i))(0) = 0, i = 1, 2, ..., n-3, n >= 3, x((n-2))(infinity) = integral(eta)(0)x((n-2))(s)dA(s), Where eta > 0, h : [0, infinity) x R-n -> R is a Caratheodory's function with A(0) = 0, A(eta) = 1, w is an element of C[0, infinity), w(t) > 0 for all t >= 0, phi(p)(s) = vertical bar s vertical bar(p-2)s.