Remarks on the Morse index theorem

Author:
William T. Reid

Journal:
Proc. Amer. Math. Soc. **20** (1969), 339-341

MSC:
Primary 57.50

DOI:
https://doi.org/10.1090/S0002-9939-1969-0234497-X

MathSciNet review:
0234497

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References | Similar Articles | Additional Information

**[1]**G. D. Birkhoff and M. R. Hestenes,*Natural isoperimetric conditions in the calculus of variations*, Duke Math. J.**1**(1935), no. 2, 198–286. MR**1545876**, https://doi.org/10.1215/S0012-7094-35-00118-1**[2]**Gilbert A. Bliss,*Lectures on the Calculus of Variations*, University of Chicago Press, Chicago, Ill., 1946. MR**0017881****[3]**Katharine Elizabeth Hazard,*Index theorems for the problem of Bolza in the calculus of variations*, Contributions to the Calculus of Variations, 1938–1941, University of Chicago Press, Chicago, Ill., 1942, pp. 293–356. MR**0006823****[4]**M. R. Hestenes,*The problem of Bolza in the calculus of variations*, Bull. Amer. Math. Soc.**48**(1942), 57–75. MR**0006021**, https://doi.org/10.1090/S0002-9904-1942-07600-2**[5]**Magnus R. Hestenes,*Applications of the theory of quadratic forms in Hilbert space to the calculus of variations*, Pacific J. Math.**1**(1951), 525–581. MR**0046590****[6]**Magnus R. Hestenes,*Quadratic variational theory and linear elliptic partial differential equations*, Trans. Amer. Math. Soc.**101**(1961), 306–350. MR**0133575**, https://doi.org/10.1090/S0002-9947-1961-0133575-0**[7]**K.-S. Hu,*The problem of Bolza and its accessory boundary value problem*, Contributions to the calculus of variations, Univ. of Chicago Press, Chicago, Ill., 1931-1932, pp. 361-444.**[8]**W. Karush,*Isoperimetric problems and index theorems in the calculus of variations*, Dissertation, Univ. of Chicago, Chicago, Ill., 1942.**[9]**Marston Morse,*The foundations of the calculus of variations in the large in 𝑚-space. I*, Trans. Amer. Math. Soc.**31**(1929), no. 3, 379–404. MR**1501489**, https://doi.org/10.1090/S0002-9947-1929-1501489-9**[10]**Marston Morse,*A generalization of the sturm separation and comparison theorems in 𝑛-space*, Math. Ann.**103**(1930), no. 1, 52–69. MR**1512617**, https://doi.org/10.1007/BF01455690**[11]**-,*The calculus of variations in the large*, Amer. Math. Soc. Colloq. Publ., Vol. 18, Amer. Math. Soc., Providence, R. I., 1934.**[12]**Howard Osborn,*The Morse index theorem*, Proc. Amer. Math. Soc.**18**(1967), 759–762. MR**0212839**, https://doi.org/10.1090/S0002-9939-1967-0212839-7**[13]**Howard Osborn,*Correction to my paper: “The Morse index theorem“*, Proc. Amer. Math. Soc.**20**(1969), 337–338. MR**0234496**, https://doi.org/10.1090/S0002-9939-1969-0234496-8**[14]**W. T. Reid,*Boundary value problems of the calculus of variations*, Bull. Amer. Math. Soc.**43**(1937), no. 10, 633–666. MR**1563613**, https://doi.org/10.1090/S0002-9904-1937-06616-X**[15]**William T. Reid,*An Integro-Differential Boundary Value Problem*, Amer. J. Math.**60**(1938), no. 2, 257–292. MR**1507311**, https://doi.org/10.2307/2371292**[16]**William T. Reid,*Variational methods and boundary problems for ordinary linear differential systems*, Proc. U.S.-Japan Seminar on Differential and Functional Equations (Minneapolis, Minn., 1967) Benjamin, New York, 1967, pp. 267–299. MR**0228743****[17]**L. Ritcey,*Index theorems for discontinuous problems in the calculus of variations*, Dissertation, Univ. of Chicago, Chicago, Ill., 1945.

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DOI:
https://doi.org/10.1090/S0002-9939-1969-0234497-X

Article copyright:
© Copyright 1969
American Mathematical Society