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@article{490806,
author = {Hilscher, Roman and Zeidan, Vera},
article_location = {San Diego (USA)},
article_number = {1},
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},
language = {eng},
issn = {0022-247X},
journal = {Journal of Mathematical Analysis and Applications},
title = {Calculus of variations on time scales: weak local piecewise C1rd solutions with variable endpoints},
volume = {289},
year = {2004}
}
TY - JOUR
ID - 490806
AU - Hilscher, Roman - Zeidan, Vera
PY - 2004
TI - Calculus of variations on time scales: weak local piecewise C1rd solutions with variable endpoints
JF - Journal of Mathematical Analysis and Applications
VL - 289
IS - 1
SP - 143-166
EP - 143-166
PB - Elsevier Science
SN - 0022247X
KW - Calculus of variations
KW - Weak local minimum
KW - Euler-Lagrange equation
KW - Calculus of variations
KW - Weak local minimum
KW - First variation
KW - Euler-Lagrange equation
KW - Transversality condition
KW - Second variation
KW - Quadratic functional
KW - Nonnegativity
KW - Coercivity
N2 - 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.
ER -
HILSCHER, Roman a Vera ZEIDAN. Calculus of variations on time scales: weak local piecewise C1rd solutions with variable endpoints. \textit{Journal of Mathematical Analysis and Applications}. San Diego (USA): Elsevier Science, roč.~289, č.~1, s.~143-166. ISSN~0022-247X. 2004.
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