Natural SciencesMathematicsDifferential EquationsMathematical PhysicsStochastic ProcessesCalculus Of VariationsPartial Differential EquationsVariational FormulationVariational PrinciplesExistence Of MinimizersTime ScalesUniqueness Of MinimizersVariational Problems
ABSTRACT. We introduce a version of the calculus of variations on time scales, which includes as special cases the classical calculus of variations and the discrete calculus of variations. Necessary conditions for weak local minima are established, among them the Euler condition, the Legendre condition, the strengthened Legendre condition, and the Jacobi condition. AMS (MOS) Subject Classification. 39A10. 1.
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