Topological transversality and boundary value problems on time scales.
The authors present some general existence theorems for solutions to \(n\)th-order boundary value problems on time scales by applying the topological transversality method. A key assumption of these general theorems is that all solutions to certain families of boundary value problems are bounded a priori. Sufficient conditions are then formulated so that all solutions to the boundary value problem under consideration will satisfy certain a priori bounds. The boundary conditions of these boundary value problems may be very general, including nonlinear and mixed variations. The results are then applied to establish existence criteria for specific second-order boundary value problems on time scales.
scientific article; zbMATH DE number 2032958
scientific article