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

MathSciNet review:
0052706

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References | Similar Articles | Additional Information

**[1]**Gilbert A. Bliss,*Lectures on the Calculus of Variations*, University of Chicago Press, Chicago, Ill., 1946. MR**0017881****[2]**Lawrence M. Graves,*The Theory of Functions of Real Variables*, McGraw-Hill Book Company, Inc., New York, 1946. MR**0018708****[3]**Magnus R. Hestenes,*The Weierstrass 𝐸-function in the calculus of variations*, Trans. Amer. Math. Soc.**60**(1946), 51–71. MR**0017478**, 10.1090/S0002-9947-1946-0017478-X**[4]**Magnus R. Hestenes,*Theorem of Lindeberg in the calculus of variations*, Trans. Amer. Math. Soc.**60**(1946), 72–92. MR**0017479**, 10.1090/S0002-9947-1946-0017479-1**[5]**Magnus R. Hestenes,*Sufficient conditions for the isoperimetric problem of Bolza in the calculus of variations*, Trans. Amer. Math. Soc.**60**(1946), 93–118. MR**0017480**, 10.1090/S0002-9947-1946-0017480-8**[6]**Magnus R. Hestenes,*An indirect sufficiency proof for the problem of Bolza in nonparametric form*, Trans. Amer. Math. Soc.**62**(1947), 509–535. MR**0023465**, 10.1090/S0002-9947-1947-0023465-9**[7]**William Karush,*Minima of functions of several variables with inequalities as side conditions*, University of Chicago Master's Thesis, 1939.**[8]**Edward James McShane,*Integration*, Princeton University Press, Princeton, N. J., 1944 1957. MR**0082536****[9]**E. J. McShane,*Sufficient conditions for a weak relative minimum in the problem of Bolza*, Trans. Amer. Math. Soc.**52**(1942), 344–379. MR**0006828**, 10.1090/S0002-9947-1942-0006828-2**[10]**William T. Reid,*Isoperimetric problems of Bolza in nonparametric form*, Duke Math. J.**5**(1939), 675–691. MR**0000100****[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