Oscillation criteria for self-adjoint differential systems
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- by William T. Reid
- Trans. Amer. Math. Soc. 101 (1961), 91-106
- DOI: https://doi.org/10.1090/S0002-9947-1961-0133518-X
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References
- N. I. Achieser and I. M. Glasmann, Theorie der linearen Operatoren im Hilbert-Raum, Akademie-Verlag, Berlin, 1954 (German). MR 0066560 J. H. Barrett, Two-point boundary value problems and comparison theorems for fourth-order self-adjoint differential equations and second-order matrix differential equations, Technical Summary Report #150, April, 1960, Mathematics Research Center, U. S. Army.
- 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, DOI 10.1215/S0012-7094-35-00118-1
- Gilbert A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Ill., 1946. MR 0017881
- Maxime Bôcher, Applications and generalizations of the conception of adjoint systems, Trans. Amer. Math. Soc. 14 (1913), no. 4, 403–420. MR 1500954, DOI 10.1090/S0002-9947-1913-1500954-6
- 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 46590
- Henry Howard, Oscillation criteria for fourth-order linear differential equations, Trans. Amer. Math. Soc. 96 (1960), 296–311. MR 117379, DOI 10.1090/S0002-9947-1960-0117379-X K. S. Hu, The problem of Bolza and its accessory boundary value problem (Dissertation, University of Chicago, 1932), Contributions to the Calculus of Variations, University of Chicago Press, 1931-1932, pp. 361-443.
- Walter Leighton, The detection of the oscillation of solutions of a second order linear differential equation, Duke Math. J. 17 (1950), 57–61. MR 32065
- Walter Leighton and Zeev Nehari, On the oscillation of solutions of self-adjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325–377. MR 102639, DOI 10.1090/S0002-9947-1958-0102639-X
- Marston Morse, Sufficient conditions in the problem of Lagrange with fixed end points, Ann. of Math. (2) 32 (1931), no. 3, 567–577. MR 1503017, DOI 10.2307/1968252
- Marston Morse, Sufficient Conditions in the Problem of Lagrange with Variable End Conditions, Amer. J. Math. 53 (1931), no. 3, 517–546. MR 1507924, DOI 10.2307/2371163 —, The calculus of variations in the large, Amer. Math. Soc. Colloquium Publications, vol. 18, 1934.
- Zeev Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957), 428–445. MR 87816, DOI 10.1090/S0002-9947-1957-0087816-8
- William T. Reid, A Boundary Value Problem Associated with the Calculus of Variations, Amer. J. Math. 54 (1932), no. 4, 769–790. MR 1506937, DOI 10.2307/2371102
- William T. Reid, An Integro-Differential Boundary Value Problem, Amer. J. Math. 60 (1938), no. 2, 257–292. MR 1507311, DOI 10.2307/2371292
- William T. Reid, A matrix differential equation of Riccati type, Amer. J. Math. 68 (1946), 237–246. MR 15610, DOI 10.2307/2371835
- William T. Reid, Oscillation criteria for linear differential systems with complex coefficients, Pacific J. Math. 6 (1956), 733–751. MR 84655
- William T. Reid, Adjoint linear differential operators, Trans. Amer. Math. Soc. 85 (1957), 446–461. MR 88625, DOI 10.1090/S0002-9947-1957-0088625-6
- William T. Reid, Principal solutions of non-oscillatory self-adjoint linear differential systems, Pacific J. Math. 8 (1958), 147–169. MR 98220
- H. M. Sternberg and R. L. Sternberg, A two-point boundary problem for ordinary self-adjoint differential equations of fourth order, Canad. J. Math. 6 (1954), 416–419. MR 61738, DOI 10.4153/cjm-1954-041-5
Bibliographic Information
- © Copyright 1961 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 101 (1961), 91-106
- MSC: Primary 34.30
- DOI: https://doi.org/10.1090/S0002-9947-1961-0133518-X
- MathSciNet review: 0133518