Equilibrium of permanent multivalued systems
Authors:
Yong Li, Huai Zhong Wang and Xian Rui Lü
Journal:
Quart. Appl. Math. 51 (1993), 791-795
MSC:
Primary 34A60; Secondary 34C05, 34D99, 92D25
DOI:
https://doi.org/10.1090/qam/1247442
MathSciNet review:
MR1247442
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Abstract: This paper is concerned with the existence problem of an equilibrium state for permanent multivalued systems. It is proved that the permanence of multivalued systems implies the existence of an equilibrium state by using the approximating technique of set-valued maps and asymptotic fixed point theory.
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T. Burton and V. Hutson, Repellers in systems with infinite delay, J. Math. Anal. Appl. 137, 240–263 (1989)
G. Butler, H. Freedman, and P. Waltman, Uniformly persistent systems, Proc. Amer. Math. Soc. 96, 425–430 (1967)
A. F. Filippov, Classical solutions of differential equations with multivalued right-hand sides, SIAM J. Control 5, 609–621 (1967)
A. F. Filippov, Differential equations with discontinuous right-hand sides, Math. Appl., Kluwer, Dordrecht, 1988
H. Freedman and J. So, Persistence in discrete semi-dynamical systems, SIAM J. Math. Anal. 20, 930–938 (1989)
P. Hartman, Ordinary Differential Equations, Birkhäuser, Boston, MA, 1982
J. Hofbauer, V. Hutson, and W. Jansen, Coexistence for systems governed by difference equations of Lotka-Volterra type, J. Math. Biol. 25, 553–570 (1987)
J. Hofbauer and K. Sigmund, Dynamical systems and the theory of evolution, Cambridge Univ. Press, London and New York, 1988
V. Hutson, A theorem on average Liapunov functions, Monatsh. Math. 98 4, 267–275 (1984)
V. Hutson, The existence of an equilibrium for permanent systems, Rocky Mountain J. Math. 20, 1033–1040 (1990)
V. Hutson and W. Moran, Persistence of species obeying difference equations, Math. Biosci. 15, 203–213 (1982)
V. Hutson and W. Moran, Repellers in reaction-diffusion systems, Rocky Mountain J. Math. 17, 301–314 (1987)
V. Hutson and J. Pym, Repellers for generalized semidynamical systems, Mathematics of Dynamic Processes (A. Kurzhanski, ed.), Lecture Notes in Econ. and Math. Systems, 287, Springer-Verlag, Berlin, 1987, pp. 39–49
G. S. Jones, Asymptotic fixed point theory, Technical Notes BN-502, University of Maryland, College Park, 1967
W. G. Kelley, Periodic solutions of generalized differential equations, SIAM J. Appl. Math. 30, 70–74 (1976)
S. Zaremba, Sur les équations au paratingent, Bull. Sci. Math. 60, 139–160 (1936)
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Article copyright:
© Copyright 1993
American Mathematical Society