A class of strongly cooperative systems without compactness

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Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, PL-50-370 Wrocław, Poland

[H1] M. W. Hirsch, Systems of differential equations that are competitive or cooperative. II: Convergence almost everywhere, SIAM J. Math. Anal. 16 (1985), 423-439.
[H2] M. W. Hirsch, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math. 383 (1988), 1-53.
[L] K. Leichtweiss, Konvexe Mengen, Springer, Berlin-New York 1980.
[M1] J. Mierczyński, Strictly cooperative systems with a first integral, SIAM J. Math. Anal. 18 (1987), 642-646.
[M2] J. Mierczyński, Finsler structures as Liapunov functions, in: Proc. Eleventh Internat. Conf. on Nonlinear Oscillations, Budapest, August 17-23, 1987, M. Farkas, V. Kertész and G. Stépán (eds.), János Bolyai Math. Soc., Budapest 1987, 447-450.
[P] P. Poláčik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Differential Equations 79 (1989), 89-110.
[S] H. L. Smith, Systems of ordinary differential equations which generate an order preserving flow. A survey of results, SIAM Rev. 30 (1988), 87-114.
[ST] H. L. Smith and H. R. Thieme, Quasi convergence and stability for strongly order-preserving semiflows, SIAM J. Math. Anal. 21 (1990), 673-692.