Dynamic boundary value problems of the second-order: Bernstein-Nagumo conditions and solvability

This article analyzes the solvability of second-order, nonlinear dynamic boundary value problems (BVPs) on time scales. New Bernstein-Nagumo conditions are developed that guarantee an a priori bound on the delta derivative of potential solutions to the BVPs under consideration. Topological methods are then employed to gain solvability.