Calculus of variations on time scales: weak local piecewise C1rd solutions with variable endpoints
| Authors | |
|---|---|
| Year of publication | 2004 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Analysis and Applications |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Calculus of variations; Weak local minimum; Euler-Lagrange equation; Calculus of variations; Weak local minimum; First variation; Euler-Lagrange equation; Transversality condition; Second variation; Quadratic functional; Nonnegativity; Coercivity |
| Description | 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 ( C1prd ). 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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