Solvability of second-order boundary-value problems at resonance involving integral conditions

This article concerns the second-order differential equation with integral boundary conditions $$displaylines{ x''(t)=f(t,x(t),x'(t)),quad tin (0,1),cr x(0)=int_0^1x(s)dalpha(s),quad x(1)=int_0^1x(s)deta(s). }$$ Under the resonance conditions, we construct a projector and then applying coincidence degree theory to establish the existence of solutions.