Remarks on the Periodic Boundary Value Problems for Nonlinear Second Order Ordinary Differential Equations

This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $\alpha (0)=\alpha (2\pi )$ and $\beta (0)=\beta (2\pi )$. We present several comparison results. We show that the method of lower and upper solutions coupled with the monotone iterative technique is valid to obtain constuctive proof of existence of solutions.