Nonlinear scalar two-point boundary-value problems on time scales - Rebecca I. B. Kalhorn (Electronic Journal of Differential Equations, 2010)
We establish sufficient conditions for the solvability of scalar nonlinear boundary-value problems on time scales. Our attention will be focused on problems where the solution space for the corresponding linear homogeneous boundary-value problem is nontrivial. As a consequence of our results we are able to provide easily verifiable conditions for the existence of periodic behavior for dynamic equations on time scales.