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

Title	Elimination of Jacobi equation in extremal variational problems
Source	Methods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 341-349
MathSciNet	MR2907362
Copyright	The Author(s) 2011 (CC BY-SA)

Authors Information

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

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},
  MRNUMBER = {MR2907362},
       URL = {http://mfat.imath.kiev.ua/article/?id=594},
}