Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions

Abstract EN

We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right member f, a Δ-Carathéodory function.

First, we consider the case where the nonlinearity f does not depend on the Δ-derivative, xΔ(t).

We obtain existence results for Strum-Liouville and for periodic boundary conditions.

Finally, we consider more general systems in which the nonlinearity f depends on the Δ-derivative and satisfies a linear growth condition with respect to xΔ(t).

Our existence results rely on notions of solution-tube that are introduced in this paper.