Composition functionals in calculus of variations. Application to products and quotients

Mathematical Models and Methods in Applied Sciences

Volumn 18, Issue 1, 2008, Pages 47-75

  Castillo, Enrique ^a   Luceño, Alberto ^a   Pedregal, Pablo ^b  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

Coercivity; Euler Lagrange equations; Market competitiveness; Natural conditions; Product functionals; Quotient functionals; Slope stability; Transversality conditions; Weak lower semicontinuity; Weierstrass Erdman conditions

Indexed keywords

FUNCTION EVALUATION; FUNCTIONAL ANALYSIS; INTEGRAL EQUATIONS; PROBLEM SOLVING;

OPTIMAL SOLUTIONS; SCALAR FUNCTIONS; WEIERSTRASS-ERDMAN CONDITIONS;

LAGRANGE MULTIPLIERS;

EID: 43949133877     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202508002607     Document Type: Article

References (29)

1. A. K. Bhunia and M. Maiti, Determinitic inventory models for variable production, J. Oper. Res. Soc. 48 (1997).
2. B. Bolza, Lectures on the Calculus of Variations (Chelsea Publishing Co., 1973).
3. B. Bonnard and J. B. Caillau, Advanced Topics in Control Systems Theory, Lecture Notes in Control and Information Sciences, eds. A. Loria, F. Lamnabhi and E, Pan-teley, Vol. 328 (Springer-Verlag, 2006), pp. 1-60.
4. E. Buckingham, The principle of similitude, Nature 96 (1915) 396-397.
5. E. Castilllo and J. Revilla, One application of the calculus of variations to the stability of slopes, in Proc. of the 9th Int. Conf. on Soil Mechanics and Foundations Engineering, Vol. 2 (Tokyo, 1977), pp. 25-30.
6. E. Castillo, A. J. Conejo and E. Aranda, Sensitivity analysis in calculus of variations some applications, SIAM Rev. 50 (2008).
7. E. Castillo and A. Luceño, A critical analysis of some variational methods in slope stability analysis, Int. J. Numer. Anal. Meth. Geomech. 6 (1982) 195-209.
8. E. Castillo and A. Luceño, Variational methods and the upper bound theorem, J. Eng. Mech. 109 (1983) 1157-1174.
9. B. Dacorogna, Direct Methods in the Calculus of Variations, Applied Mathematical Sciences, Vol. 78 (Springer-Verlag, 1989).
10. B. Dacorogna, Introduction au Calcul des Variations, Cahiers Mathématiques de l'École Polytechnique Fédérale de Lausanne, Vol. 3 (Presses Polytechniques et Universitaires Romandes, 1992).
11. B. Dacorogna, Introduction to the Calculus of Variations (Imperial College Press, 2004).
12. L. Elsgolc, Calculus of Variations (Pergamon Press, 1962).
13. L. Euler, Metod Nakhozhdeniia Krivykh Linii, Obladiaiushchikh Svoistvami Maksi-muma Libo Minimuma, Ili Reshenie Izoperimetricheskoi Zadachi Vziatoi v Samom Shirokom Smysle (GITTL 1744).
14. M. J. Forray, Variational Calculus in Science and Engineering (Mc Graw-Hill, 1968).
15. A. R. Forsyth, Calculus of Variations (Dover, 1960).
16. M. Garber, Variational methods for investigating the stability of slopes, Soil Mech. Found. Eng. 10 (1973) 77-79.
17. I. M. Gelfand and S. V. Fomin, Calculus of Variations (Prentice Hall, 1963).
18. M. Giaquinta and S. Hildebrandt, Calculus of Variations. Vol. 1: The Lagrangian Formalism (Springer-Verlag, 1995).
19. M. Giaquinta and S. Hildebrandt, Calculus of Variations. Vol. 2: The Hamiltonian Formalism (Springer-Verlag, 1995).
20. H. H. Goldstine, A History of the Calculus of Variations from the 17th to the 19th Century (Springer-Verlag, 1980).
21. N. Janbu, Earth pressure and bearing capacity calculations by generalized procedure of slices, In Proc. of the 4th Int. Conf. on Soil Mechanics and Foundations Engineering (1957).
22. A. Luceño, Análisis de los métodos variacionales aplicados a los problemas de estabil-idad en Mecánica del suelo. Utilización del teorema de la cota superior, PhD thesis, Escuela de ingenieros de Caminos, Canales y Puertos. University of Cantabria, Santander, Spain (1979).
23. C R. MacCluer, Calculus of Variations. Mechanics, Control, and Other Applications (Pearson Prentice Hall, 2005).
24. P. Pedregal, Nonlocal variational principles, Nonlinear Anal. 29 (1997) 1379-1392.
25. P. Pedregal, Parametrized Measures and Variational Principles, 1st edn. (Birkhauser-Verlag, 1997).
26. I. P. Petrov, Variational Methods in Optimum Control Theory (Academic Press, 1968).
27. J. Revilla and E. Castillo, The calculus of variations applied to stability of slopes, Geotech. 27 (1977) 1-11.
28. W. Wamae, A technology acquisition model: The role of learning and innovation. Technical Report 2006-022, United Nations University.
29. R. Woodhouse, History of the Calculus of Variations in the 18th Century (Chelsea Publishing Co., 1975).