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Book Review
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Book Information
Author(s):
Hal L. Smith
Title:
Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems
Additional book information:
Mathematical Surveys and Monographs, vol. 41,
Amer. Math. Soc., Providence, RI,
1995,
x + 174,
$49.00,
0-8218-0393-X
References:
- [1]
- R. Courant and D. Hilbert, Methoden der Mathematischen Physik, vol. 2, Springer-Verlag, Berlin, 1937.
- [2]
- P. Hess, Periodic-parabolic boundary value problems and positivity, Longman Scientific and Technical, New York, 1991.MR 92h:35001
- [3]
- M. Hirsch, Differential equations and convergence almost everywhere in strongly monotone flows, Contemporary Mathematics vol. 17 (J. Smoller, ed.), Amer. Math. Soc., Providence, RI, 1983, pp. 267--285. MR 84h:34095
- [4]
- ------, The dynamical systems approach to differential equations, Bull. Amer. Math. Soc. (N.S.) 11 (1984), 1--64. MR 85m:58060
- [5]
- ------, Systems of differential equations that are competitive or cooperative II: Convergence almost everywhere, SIAM J. Math. Anal. 16 (1985), 423--439.MR 87a:58137
- [6]
- ------, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math. 383 (1988), 1--53.MR 89c:58108
- [7]
- E. Kamke, Zur Theorie der Systeme gewöhnlicher Differentialgleichungen II, Acta Math. 58 (1932), 57--85.
- [8]
- A. Leung, Systems of nonlinear partial differential equations, Kluwer Academic Publishers, Boston, 1989.
- [9]
- H. Matano, Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems, J. Fac. Sci. Univ. Tokyo 30 (1984), 645--673.MR 85d:35014
- [10]
- C.-V. Pao, Nonlinear parabolic and elliptic equations, Plenum Press, New York, 1992.MR 94c:35002
- [11]
- M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, NJ, 1967.MR 36:2935
- [12]
- H. Smith, Systems of ordinary differential equations which generate an order preserving flow. A survey of results, SIAM Rev. 30 (1988), 87--113.MR 89f:34065
- [13]
- H. Smith and H. Thieme, Monotone semiflows in scalar non-quasi-monotone functional differential equations, J. Math. Anal. Appl. 150 (1990), 289--306.MR 91j:34117
- [14]
- ------, Strongly order preserving semiflows generated by functional differential equations, J. Diff. Equations 93 (1991), 332--363. MR 93f:34135
- [15]
- J. Smoller, Shock waves and reaction-diffusion equations, 2nd ed., Springer, New York, 1994. CMP 95:03
Additional Information:
Reviewer(s):
Chris
Cosner
Affiliation:
University of Miami
Email:
gcc@paris-gw.cs.miami.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
33
(1996),
203-209.
DOI:
10.1090/S0273-0979-96-00642-8
PII:
S 0273-0979(96)00642-8
Copyright of article:
Copyright
1996,
American Mathematical Society
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