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Multiparameter bifurcation for some particular reaction–diffusion systems

Published online by Cambridge University Press:  14 November 2011

J. Esquinas
Affiliation:
Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
J. López-Gómez
Affiliation:
Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain

Synopsis

In some cases, a reaction–diffusion system can be transformed into an abstract equation where the linear part is given by a polynomial of a linear operator, say Multiparameter bifurcation for this equation is considered as the coefficients of the operator polynomial in are varied.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1.Amraoui, S. and Labani, H.. Etude de la bifurcation pour Anal. Nonlineaire, Besangon 9 (1986), 112134.Google Scholar
2.Crandall, M. G. and Rabinowitz, P. H.. Bifurcation from simple eigenvalues. J. Funct. Anal. 8 (1971), 321340.CrossRefGoogle Scholar
3.Esquinas, J. and López-Gómez, J.. Optimal multiplicity in local bifurcation theory. In Contributions to Nonlinear Partial Differential Equations, Vol. II, eds Diaz, J. I. and Lions, P. L., pp. 103110 (London: Pitman, 1987).Google Scholar
4.Esquinas, J. and López-Gómez, J.. Optimal multiplicity in local bifurcation theory. Part I: Generalized generic eigenvalues. J. Differential Equations 71 (1988), 7292.CrossRefGoogle Scholar
5.Fife, P. C.. Mathematical Aspects of Reacting and Diffusing Systems. Lecture Notes in Biomathematics 28 (New York: Springer, 1979).CrossRefGoogle Scholar
6.Gantmacher, F. R.. Théorie des Matrices, Tome I. (Paris: Dunod, 1966).Google Scholar
7.Goldberg, S.. Unbounded Linear Operators (New York: McGraw-Hill, 1966).Google Scholar
8.Ize, J.. Bifurcation theory for Fredholm operators. Mem. Amer. Math. Soc. 7 (1976).Google Scholar
9.López-Gómez, J. and Pardo, R.. Multiparameter nonlinear eigenvalues problems. Positive solutions to elliptic Lotka–Volterra systems (preprint).Google Scholar
10.Murray, J. D.. Nonlinear Differential Equations Models in Biology (Oxford: Clarendon Press, 1977).Google Scholar