# Examples from the calculus of variations. IV. Concluding review

Mathematica Bohemica (2001)

- Volume: 126, Issue: 4, page 691-710
- ISSN: 0862-7959

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topChrastina, Jan. "Examples from the calculus of variations. IV. Concluding review." Mathematica Bohemica 126.4 (2001): 691-710. <http://eudml.org/doc/248868>.

@article{Chrastina2001,

abstract = {Variational integrals containing several functions of one independent variable subjected moreover to an underdetermined system of ordinary differential equations (the Lagrange problem) are investigated within a survey of examples. More systematical discussion of two crucial examples from Part I with help of the methods of Parts II and III is performed not excluding certain instructive subcases to manifest the significant role of generalized Poincaré-Cartan forms without undetermined multipliers. The classical Weierstrass-Hilbert theory is simulated to obtain sufficient extremality conditions. Unlike the previous parts, this article is adapted to the category of continuous objects and mappings without any substantial references to the general principles, which makes the exposition self-contained.},

author = {Chrastina, Jan},

journal = {Mathematica Bohemica},

keywords = {Lagrange problem; Poincaré-Cartan form; Hamiltonian-Jacobi equation; Weierstrass-Hilbert method; Lagrange problem; Poincaré-Cartan form; Hamilton-Jacobi equation; Weierstrass-Hilbert method},

language = {eng},

number = {4},

pages = {691-710},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Examples from the calculus of variations. IV. Concluding review},

url = {http://eudml.org/doc/248868},

volume = {126},

year = {2001},

}

TY - JOUR

AU - Chrastina, Jan

TI - Examples from the calculus of variations. IV. Concluding review

JO - Mathematica Bohemica

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 126

IS - 4

SP - 691

EP - 710

AB - Variational integrals containing several functions of one independent variable subjected moreover to an underdetermined system of ordinary differential equations (the Lagrange problem) are investigated within a survey of examples. More systematical discussion of two crucial examples from Part I with help of the methods of Parts II and III is performed not excluding certain instructive subcases to manifest the significant role of generalized Poincaré-Cartan forms without undetermined multipliers. The classical Weierstrass-Hilbert theory is simulated to obtain sufficient extremality conditions. Unlike the previous parts, this article is adapted to the category of continuous objects and mappings without any substantial references to the general principles, which makes the exposition self-contained.

LA - eng

KW - Lagrange problem; Poincaré-Cartan form; Hamiltonian-Jacobi equation; Weierstrass-Hilbert method; Lagrange problem; Poincaré-Cartan form; Hamilton-Jacobi equation; Weierstrass-Hilbert method

UR - http://eudml.org/doc/248868

ER -

## References

top- Examples from the calculus of variations I. Nondegenerate problems, Math. Bohem. 125 (2000), 55–76. (2000) Zbl0968.49001MR1752079
- The Mayer problem, (to appear). (to appear)
- On a degenerate variational problem, (to appear). (to appear)

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