An indirect sufficiency proof for the problem of Lagrange with differential inequalities as added side conditions

Author:
Louis L. Pennisi

Journal:
Trans. Amer. Math. Soc. **74** (1953), 177-198

MSC:
Primary 49.0X

DOI:
https://doi.org/10.1090/S0002-9947-1953-0052706-X

MathSciNet review:
0052706

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References | Similar Articles | Additional Information

**[1]**Gilbert A. Bliss,*Lectures in the calculus of variations*, University of Chicago Press, 1946. MR**0017881 (8:212e)****[2]**Lawrence M. Graves,*Theory of functions of real variables*, McGraw-Hill, 1946. MR**0018708 (8:319d)****[3]**M. R. Hestenes,*The Weierstrass -function in the calculus of variations*, Trans. Amer. Math. Soc. vol. 60 (1946) pp. 51-71. MR**0017478 (8:160b)****[4]**-,*Theorem of Lindberg in the calculus of variations*, ibid. pp. 72-92. MR**0017479 (8:160c)****[5]**-,*Sufficient conditions for the isoperimetric problem of Bolza in the calculus of variations*, ibid. pp. 93-118. MR**0017480 (8:160d)****[6]**-,*An indirect sufficiency proof for the problem of Bolza in nonparametric form*, ibid. vol. 62 (1947) pp. 509-535. MR**0023465 (9:360c)****[7]**William Karush,*Minima of functions of several variables with inequalities as side conditions*, University of Chicago Master's Thesis, 1939.**[8]**E. J. McShane,*Integration*, Princeton University Press, 1944. MR**0082536 (18:567a)****[9]**-,*Sufficient conditions for a weak relative minimum in the problem of Bolza*, Trans. Amer. Math. Soc. vol. 52 (1942) pp. 344-379. MR**0006828 (4:48d)****[10]**W. T. Reid,*Isoperimetric problems of Bolza in nonparametric form*, Duke Math. J. vol. 5 (1939) pp. 675-691. MR**0000100 (1:19b)****[11]**Frederick A. Valentine,*The problem of Lagrange with differential inequalities as added side conditions*, Contributions to the Calculus of Variations 1933-37, University of Chicago Press.

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DOI:
https://doi.org/10.1090/S0002-9947-1953-0052706-X

Article copyright:
© Copyright 1953
American Mathematical Society