Existence result of second-order differential equations with integral boundary conditions at resonance

By using Mawhin's continuation theorem, some sufficient conditions for the existence of solution for a class of second-order differential equations with integral boundary conditions at resonance are established, which are complement of previously known results. The interesting point is that we shall deal with the case dimKerL=2, which will cause some difficulties in constructing the projector Q. Since all the existence results obtained in previous papers are for the case dimKerL=1, our work is new.