Calculus of variations on time scales: weak local piecewise C1rd solutions with variable endpoints

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Authors	HILSCHER Roman ZEIDAN Vera
Year of publication	2004
Type	Article in Periodical
Magazine / Source	Journal of Mathematical Analysis and Applications
MU Faculty or unit	Faculty of Science
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.
Related projects:	Qualitative theory of solutions of difference equations