A monotone property of the solution of a stochastic boundary value problem
Author:
William B. Day
Journal:
Quart. Appl. Math. 28 (1970), 411-425
MSC:
Primary 60.75
DOI:
https://doi.org/10.1090/qam/268979
MathSciNet review:
268979
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N. Aronszajn and K. T. Smith, Characterization of positive reproducing kernels. Applications to Green’s functions, Amer. J. Math. 79, 611–622 (1957)
R. Bellman, On the nonnegalivity of Green’s function, Boll. Un. Mat. Ital. (3) 12, 411–413 (1957)
R. Bellman, On the nonnegativity of Green’s function, Boll. Un. Mat. Ital. (3) 18, 219–221 (1963)
A. T. Bharucha-Reid, On the theory of random equations, Proc. Sympos. Appl. Math., vol. 16, Amer. Math. Soc., Providence, R. I., 1964, pp. 40–69
W. E. Boyce, Random vibration of elastic strings and bars, Proc. Fourth U. S. Nat. Congr. Appl. Mech. (Univ. California, Berkeley, Calif., 1962) vol. 1, Amer. Soc. Mech. Engrs., New York, 1962, pp. 77–85
W. E. Boyce and B. E. Goodwin, Random transverse vibrations of elastic beams, SIAM J. 12, 613–629 (1964)
W. E. Boyce, Stochastic nonhomogeneous Sturm-Liouville problems, J. Franklin Inst. 282, 206–215 (1966)
V. A. Čurikov, Conditions for the existence and preservation of the sign of the Green’s function of a two-point boundary value problem, Izv. Vysš. Učebn. Zaved. Matematika, 1967, no. 257, 93–99 (Russian)
B. E. Goodwin and W. E. Boyce, Vibrations of random elastic strings: method of integral equations, Quart. Appl. Math., 22, 261–266 (1964)
C. W. Haines, An analysis of stochastic eigenvalue problems, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, New York, 1965
C. W. Haines, Hierarchy methods for random vibrations of elastic strings and beams, Proc. Fifth U. S. Nat. Congr. Appl. Mech., Minneapolis, 1966
E. L. Ince, Ordinary differential equations, Longmans, Green & Company, London, 1927; reprint: Dover, New York, 1945
D. Middleton, An introduction to statistical communication theory, McGraw-Hill, New York, 1960
S. A. Pak, Sign-preserving conditions for the Green’s function of a Sturm-Liouville problem, Dokl. Akad. Nauk SSSR 148, 1265–1267 (1963)-Soviet Math. Dokl. 4, 276–279(1963)
M. H. Protter and H. G. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1967
C. A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York, 1968
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© Copyright 1970
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