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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 nonlinearityfdoes not depend on theΔ-derivative,xΔ(t). We obtain existence results for Strum-Liouville and for periodic boundary conditions. Finally, we consider more general systems in which the nonlinearityfdepends on theΔ-derivative and satisfies a linear growth condition with respect toxΔ(t). Our existencedoi:10.1155/2010/234015 fatcat:xufvwlrg4rcv3kyemyafvydon4