Solutions of periodic boundary value problems

We deal with a resonant boundary value problem involving a second-order differential equation with periodic boundary conditions. First, we modify the problem at resonance and consider an equivalent nonresonant boundary value problem. Next, we obtain sufficient conditions for the existence of solutions of the modified boundary value problem, using fixed-point theory. Consequently, these conditions suffice for the existence of solutions of the original boundary value problem. We demonstrate the applicability of established results through examples.