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

HILSCHER, Roman and Vera ZEIDAN. Calculus of variations on time scales: weak local piecewise C1rd solutions with variable endpoints. Journal of Mathematical Analysis and Applications. San Diego (USA): Elsevier Science, 2004, vol. 289, No 1, p. 143-166. ISSN 0022-247X.

Basic information

Original name

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

Name in Czech

Variační počet na "time scales": slabé lokální C1rd řešení a proměnné konce

Authors

HILSCHER, Roman (203 Czech Republic, guarantor) and Vera ZEIDAN (840 United States of America)

Edition

Journal of Mathematical Analysis and Applications, San Diego (USA), Elsevier Science, 2004, 0022-247X

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Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 0.490

RIV identification code

RIV/00216224:14310/04:00011344

Organization unit

Faculty of Science

UT WoS

000187346400012

Keywords in English

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

Tags

calculus of variations, Coercivity, Euler-Lagrange equation, First variation, Nonnegativity, Quadratic functional, Second variation, Transversality condition, Weak local minimum

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Abstract

V originále

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.

In Czech

Studujeme nelineární problém variačního počtu na "time scales" s obecnými proměnnými konci. Prostor uvažovaných funkcí je prostor po částech rd-spojitě \Delta -diferencovatelných funkcí( C1prd ). Pro tento problém odvodíme Euler-Lagrangeovu rovnici, podmínku transversality a nezápornost druhé variace jakožto nutné podmínky pro slabou lokální optimalitu. Za předpokladu koercivity druhé variace dokážeme příslušné postačující kritérium druhého řádu.

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Links

GA201/01/0079, research and development project

Name: Kvalitativní teorie řešení diferenčních rovnic Investor: Czech Science Foundation, Qualitative theory of solutions of difference equations