Title:

Examples from the calculus of variations. IV. Concluding review (English) 
Author:

Chrastina, Jan 
Language:

English 
Journal:

Mathematica Bohemica 
ISSN:

08627959 (print) 
ISSN:

24647136 (online) 
Volume:

126 
Issue:

4 
Year:

2001 
Pages:

691710 
Summary lang:

English 
. 
Category:

math 
. 
Summary:

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 PoincaréCartan forms without undetermined multipliers. The classical WeierstrassHilbert 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 selfcontained. (English) 
Keyword:

Lagrange problem 
Keyword:

PoincaréCartan form 
Keyword:

HamiltonianJacobi equation 
Keyword:

WeierstrassHilbert method 
MSC:

4901 
MSC:

4902 
MSC:

49K27 
MSC:

49K45 
MSC:

58E30 
idZBL:

Zbl 1008.49015 
idMR:

MR1869462 
DOI:

10.21136/MB.2001.134113 
. 
Date available:

20090924T21:56:05Z 
Last updated:

20200729 
Stable URL:

http://hdl.handle.net/10338.dmlcz/134113 
. 
Reference:

[1] J. Chrastina: Examples from the calculus of variations I. Nondegenerate problems.Math. Bohem. 125 (2000), 55–76. Zbl 0968.49001, MR 1752079 
Reference:

[2] V. Chrastinová, V. Tryhuk: The Mayer problem.(to appear). 
Reference:

[3] V. Tryhuk: On a degenerate variational problem.(to appear). 
. 