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
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- N. Aronszajn and K. T. Smith, Characterization of positive reproducing kernels. Applications to Green’s functions, Amer. J. Math. 79 (1957), 611–622. MR 88706, DOI https://doi.org/10.2307/2372565
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. XVI, Amer. Math. Soc., Providence, R.I., 1964, pp. 40–69. MR 0189071
- W. E. Boyce, Random vibration of elastic strings and bars, Proc. 4th U.S. Nat. Congr. Appl. Mech. (Univ. California, Berkeley, Calif., 1962) Amer. Soc. Mech. Engrs., New York, 1962, pp. 77–85. MR 0152193
- William E. Boyce and Bruce E. Goodwin, Random transverse vibrations of elastic beams, J. Soc. Indust. Appl. Math. 12 (1964), 613–629. MR 175396
- William E. Boyce, Stochastic nonhomogeneous Sturm-Liouville problems, J. Franklin Inst. 282 (1966), 206–215. MR 204797, DOI https://doi.org/10.1016/0016-0032%2866%2990563-1
- 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 (1967), no. 2 (57), 93–99 (Russian). MR 0209544
B. E. Goodwin and W. E. Boyce, Vibrations of random elastic strings: method of integral equations, Quart. Appl. Math., 22, 261–266 (1964)
- Charles Wills Haines, AN ANALYSIS OF STOCHASTIC EIGENVALUE PROBLEMS, ProQuest LLC, Ann Arbor, MI, 1965. Thesis (Ph.D.)–Rensselaer Polytechnic Institute. MR 2615373
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, Dover Publications, New York, 1944. MR 0010757
- David Middleton, An introduction to statistical communication theory, International Series in Pure and Applied Physics, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR 0118561
- S. A. Pak, Sign-preserving conditions for the Green’s function of a Sturm-Liouville problem, Dokl. Akad. Nauk SSSR 148 (1963), 1265–1267 (Russian). MR 0145139
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
- C. A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York-London, 1968. Mathematics in Science and Engineering, Vol. 48. MR 0463570
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
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
60.75
Retrieve articles in all journals
with MSC:
60.75
Additional Information
Article copyright:
© Copyright 1970
American Mathematical Society
