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

M. Frigon and H. Gilbert

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: 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.

Date: 2010
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https://doi.org/10.1155/2010/234015

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:234015

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