Coupled intervals in the discrete calculus of variations:
necessity and sufficiency

J 2002

Coupled intervals in the discrete calculus of variations: necessity and sufficiency

HILSCHER, Roman a Vera ZEIDAN

Základní údaje

Originální název

Coupled intervals in the discrete calculus of variations: necessity and sufficiency

Autoři

HILSCHER, Roman a Vera ZEIDAN

Vydání

Journal of Mathematical Analysis and Applications, USA, Acad.Press, 2002, 0022-247X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.458

Kód RIV

RIV/00216224:14310/02:00008169

Organizační jednotka

Přírodovědecká fakulta

UT WoS

000179972600027

Klíčová slova anglicky

discrete quadratic functional; coupled interval; Jacobi difference equation; conjugate interval; Legendre condition; discrete calculus of variations

Štítky

conjugate interval, Coupled interval, discrete calculus of variations, discrete quadratic functional, Jacobi difference equation, Legendre condition

Změněno: 26. 6. 2009 07:44, prof. RNDr. Roman Šimon Hilscher, DSc.

Anotace

V originále

In this work we study nonnegativity and positivity of a discrete quadratic functional with separately varying endpoints. We introduce a notion of an interval coupled with 0, and hence, extend the notion of conjugate interval to 0 from the case of fixed to variable endpoint(s). We show that the nonnegativity of the discrete quadratic functional is equivalent to each of the following conditions: the nonexistence of intervals coupled with 0, the existence of a solution to Riccati matrix equation and its boundary conditions. Natural strengthening of each of these conditions yields a characterization of the positivity of the discrete quadratic functional. Since the quadratic functional under consideration could be a second variation of a discrete calculus of variations problem with varying endpoints, we apply our results to obtain necessary and sufficient optimality conditions for such problems. This paper generalizes our recent work in [18], where the right endpoint is fixed.

Návaznosti

GA201/01/0079, projekt VaV

Název: Kvalitativní teorie řešení diferenčních rovnic

Investor: Grantová agentura ČR, Kvalitativní teorie řešení diferenčních rovnic

Citovat

HILSCHER, Roman a Vera ZEIDAN. Coupled intervals in the discrete calculus of variations: necessity and sufficiency. Journal of Mathematical Analysis and Applications. USA: Acad.Press, 2002, roč. 276, č. 1, s. 396-421. ISSN 0022-247X.

@article{488395,
   author = {Hilscher, Roman and Zeidan, Vera},
   article_location = {USA},
   article_number = {1},
   keywords = {discrete quadratic functional; coupled interval; Jacobi difference equation; conjugate interval; Legendre condition; discrete calculus of variations},
   language = {eng},
   issn = {0022-247X},
   journal = {Journal of Mathematical Analysis and Applications},
   title = {Coupled intervals in the discrete calculus of variations: necessity and sufficiency},
   volume = {276},
   year = {2002}
}

TY  - JOUR
ID  - 488395
AU  - Hilscher, Roman - Zeidan, Vera
PY  - 2002
TI  - Coupled intervals in the discrete calculus of variations: necessity and sufficiency
JF  - Journal of Mathematical Analysis and Applications
VL  - 276
IS  - 1
SP  - 396-421
EP  - 396-421
PB  - Acad.Press
SN  - 0022247X
KW  - discrete quadratic functional
KW  - coupled interval
KW  - Jacobi difference equation
KW  - conjugate interval
KW  - Legendre condition
KW  - discrete calculus of variations
N2  - In this work we study nonnegativity and positivity of a discrete quadratic functional with separately varying endpoints. We introduce a notion of an interval coupled with 0, and hence, extend the notion of conjugate interval to 0 from the case of fixed to variable endpoint(s). We show that the nonnegativity of the discrete quadratic functional is equivalent to each of the following conditions: the nonexistence of intervals coupled with 0, the existence of a solution to Riccati matrix equation and its boundary conditions. Natural strengthening of each of these conditions yields a characterization of the positivity of the discrete quadratic functional. Since the quadratic functional under consideration could be a second variation of a discrete calculus of variations problem with varying endpoints, we apply our results to obtain necessary and sufficient optimality conditions for such problems. This paper generalizes our recent work in [18], where the right endpoint is fixed.
ER  -

HILSCHER, Roman a Vera ZEIDAN. Coupled intervals in the discrete calculus of variations: necessity and sufficiency. \textit{Journal of Mathematical Analysis and Applications}. USA: Acad.Press, 2002, roč.~276, č.~1, s.~396-421. ISSN~0022-247X.

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