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Book Review

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MathSciNet review: 1319817
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Book Information:

Author: 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 pp., ISBN 0-8218-0393-X, $49.00

References [Enhancements On Off] (What's this?)

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  • [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

Review Information:

Reviewer: Chris Cosner
Affiliation: University of Miami
Journal: Bull. Amer. Math. Soc. 33 (1996), 203-209
Review copyright: © Copyright 1996 American Mathematical Society
American Mathematical Society