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Elimination of Jacobi equation in extremal variational problems


Abstract

It is shown that the extremal problem for the one-dimensional Euler-Lagrange variational functional in ${C^1[a;b]}$ under a strengthened Legendre condition can be solved without using the Jacobi equation. In this case, exactly one of the two possible cases requires a restriction to the length of $[a;b]$, defined only by the form of the integrand. The result is extended to the case of compact extremum in ${H^1[a;b]}$.


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Article Information

TitleElimination of Jacobi equation in extremal variational problems
SourceMethods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 341-349
MathSciNet MR2907362
CopyrightThe Author(s) 2011 (CC BY-SA)

Authors Information

I. V. Orlov
Taurida National V.Vernadsky University, 4, Vernadsky ave., Simferopol, 95007, Ukraine 


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Citation Example

I. V. Orlov, Elimination of Jacobi equation in extremal variational problems, Methods Funct. Anal. Topology 17 (2011), no. 4, 341-349.


BibTex

@article {MFAT594,
    AUTHOR = {Orlov, I. V.},
     TITLE = {Elimination of Jacobi equation in extremal variational problems},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {17},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {341-349},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=594},
}


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