论文信息 - On Cooperative Systems with Respect to Arbitrary Orderings

On Cooperative Systems with Respect to Arbitrary Orderings

We derive conditions for cooperativity of ordinary differential equations with respect to an arbitrary order cone and generalize the classical results of M. Muller and E. Kamke to this situation. Some examples and applications are presented.

S. Walcher

[1] Max b. Müller. Über das Fundamentaltheorem in der Theorie der gewöhnlichen Differentialgleichungen , 1927 .

[2] E. Kamke. Zur Theorie der Systeme gewöhnlicher Differentialgleichungen. II. , 1932 .

[3] W. Walter. Differential and Integral Inequalities , 1970 .

[4] P. Volkmann. Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen , 1972 .

[5] W. Reid,et al. Riccati Differential Equations , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[6] M. Hirsch. Systems of di erential equations which are competitive or cooperative I: limit sets , 1982 .

[7] Hal L. Smith. Competing subcommunities of mutualist and a generalized Kamke theorem , 1986 .

[8] Robert J. Plemmons,et al. Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[9] J. Faraut,et al. Analysis on Symmetric Cones , 1995 .

[10] M. Koecher,et al. The Minnesota Notes on Jordan Algebras and Their Applications , 1999 .

[11] Herb Kunze,et al. Monotonicity with respect to closed convex cones II , 2001 .