Calculus of variations on time scales: weak local piecewise C-rd(1) solutions with variable endpoints

摘要

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 Delta-differentiable functions (C-prd(1)). 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. (C) 2003 Elsevier Inc. All rights reserved. [References: 23]