Existence result for a singular nonlinear boundary value problem at resonance Original Research Article

We study the existence of solutions of the second-order boundary value problems View the MathML sourceu″(t)+π2u(t)+a(t)g(u(t))=h(t),a.e. t∈(0,1), Turn MathJax on View the MathML sourceu′∈ACloc(0,1), Turn MathJax on u(0)=u(1)=0,u(0)=u(1)=0, Turn MathJax on where g:R→Rg:R→R is continuous, View the MathML sourcea,h∈{z∈Lloc1(0,1)∣∫01t|z(t)|dt<∞}. The proof of the main result is based upon the Lyapunov–Schmidt procedure and the connectivity properties of the solution set of parametrized families of compact vector fields.