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, 1-26

Abstract:

We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right member 𠑓 , a Δ -Carathéodory function. First, we consider the case where the nonlinearity 𠑓 does not depend on the Δ -derivative, 𠑥 Δ ( 𠑡 ). We obtain existence results for Strum-Liouville and for periodic boundary conditions. Finally, we consider more general systems in which the nonlinearity 𠑓 depends on the Δ -derivative and satisfies a linear growth condition with respect to 𠑥 Δ ( 𠑡 ). Our existence results rely on notions of solution-tube that are introduced in this paper.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:234015

DOI: 10.1155/2010/234015

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