Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions. (12th December 2010) - Frigon, M.; Gilbert, H.
Abstract : We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right memberf, aΔ -Carathéodory function. First, we consider the case where the nonlinearityf does not depend on theΔ -derivative, x Δ (t ). We obtain existence results for Strum-Liouville and for periodic boundary conditions. Finally, we consider more general systems in which the nonlinearityf depends on theΔ -derivative and satisfies a linear growth condition with respect tox Δ (t ). Our existence results rely on notions of solution-tube that are introduced in this paper.