Open Access

# 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 ${H^1[a;b]}$.

### 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)

I. V. Orlov

### 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},
}