|
|||||
|
|
Calculus of variations on time scales: weak local piecewise Crd solutions with variable endpoints |
|
| Authors: | Roman Hilscher Vera Zeidan |
| Institution: | Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA |
| 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 (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. |
| Keywords: | Calculus of variations Weak local minimum First variation Euler-Lagrange equation Transversality condition Second variation Quadratic functional Nonnegativity Coercivity |
| 本文献已被 ScienceDirect 等数据库收录！ | |