Citation: Gerardo Sánchez Licea. Sufficiency for singular trajectories in the calculus of variations[J]. AIMS Mathematics, 2020, 5(1): 111-139. doi: 10.3934/math.2020008
[1] | G. A. Bliss, Lectures on the Calculus of Variations, Chicago: University of Chicago Press, 1946. |
[2] | O. Bolza, Lectures on the Calculus of Variations, New York: Chelse Press, 1961. |
[3] | U. Brechtken-Manderscheid, Introduction to the Calculus of Variations, London: Chapman & Hall, 1983. |
[4] | L. Cesari, Optimization-Theory and Applications, Problems with Ordinary Differential Equations, New York: Springer-Verlag, 1983. |
[5] | F. H. Clarke, Functional Analysis, Calculus of Variations and Optimal Control, New York: Springer-Verlag, 2013. |
[6] | G. M. Ewing, Calculus of Variations with Applications, New York: Dover, 1985. |
[7] | I. M. Gelfand, S. V. Fomin, Calculus of Variations, New Jersey: Prentice-Hall, 1963. |
[8] | M. Giaquinta, S. Hildebrant, Calculus of Variations I, New York: Springer-Verlag, 2004. |
[9] | M. Giaquinta, S. Hildebrant, Calculus of Variations II, New York: Springer-Verlag, 2004. |
[10] | M. R. Hestenes, Calculus of Variations and Optimal Control Theory, New York: John Wiley & Sons, 1966. |
[11] | G. Leitmann, The Calculus of Variations and Optimal Control, New York: Plenum Press, 1981. |
[12] | P. D. Loewen, Second-order sufficiency criteria and local convexity for equivalent problems in the calculus of variations, J. Math. Anal. Appl., 146 (1990), 512-522. |
[13] | A. A. Milyutin, N. P. Osmolovskii, Calculus of Variations and Optimal Control, Rhode Island: American Mathematical Society, 1998. |
[14] | M. Morse, Variational Analysis: Critical Extremals and Sturmian Extensions, New York: John Wiley & Sons, 1973. |
[15] | F. Rindler, Calculus of Variations, Coventry: Springer, 2018. |
[16] | J. L. Troutman, Variational Calculus with Elementary Convexity, New York: Springer-Verlag, 1983. |
[17] | F. Y. M. Wan, Introduction to the Calculus of Variations and its Applications, New York: Chapman & Hall, 1995. |