Abstract
A nonlinear calculus of variations problem on time scales with variable endpoints is considered. The space of functions employed is that of piecewise rd-continuously Δ-differentiable functions ( C 1 prd). For this problem, the Euler–Lagrange equation, the transversality condition, and the accessory problem are derived as necessary conditions for weak local optimality. Assuming the coercivity of the second variation, a corresponding second order sufficiency criterion is established.
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