scholarly journals Isoperimetric problems of the calculus of variations on time scales

2010 ◽  
pp. 123-131 ◽  
Author(s):  
Rui A. C. Ferreira ◽  
Delfim F. M. Torres
Keyword(s):  
Calculus Of Variations ◽  
Time Scales ◽  
Isoperimetric Problems

Isoperimetric Problems in the Calculus of Variations

1952 ◽  
Vol 4 ◽  
pp. 257-280 ◽  
Author(s):  
William Karush
Keyword(s):  
Calculus Of Variations ◽  
Classical Theory ◽  
Indirect Method ◽  
Direct Method ◽  
Isoperimetric Problems ◽  
End Points ◽  
Sufficiency Theorems ◽  
Theory Of Fields ◽  
A Direct Method ◽  
Problem Of Bolza

We are concerned with establishing sufficiency theorems for minima of simple integrals of the parametric type in a class of curves with variable end points and satisfying isoperimetric side conditions. The results which are obtained involve no explicit assumptions of normality. Such results can be derived by transforming our problem to a problem of Bolza and using the latest developments in the theory of that problem. More recently [6] an indirect method of proof has been published. Our object is to present a direct method of proof without transformation of the problem which is based upon a generalization of the classical theory of fields.

scholarly journals Calculus of variations on time scales: applications to economic models

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Małgorzata Guzowska ◽  
Agnieszka B Malinowska ◽  
Moulay Rchid Sidi Ammi
Keyword(s):  
Calculus Of Variations ◽  
Time Scales ◽  
Economic Models

scholarly journals Calculus of variations on time scales with nabla derivatives

2009 ◽  
Vol 71 (12) ◽  
pp. e763-e773 ◽  
Author(s):  
Natália Martins ◽  
Delfim F.M. Torres
Keyword(s):  
Calculus Of Variations ◽  
Time Scales
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