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

By using Mawhinʹs 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 dim Ker L = 2 , which will cause some difficulties in constructing the projector Q. Since all the existence results obtained in previous papers are for the case dim Ker L = 1 , our work is new.