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On the theory of one-sided models in spaces with arbitrary cones

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  • A. A. Martynyuk
  • A. Yu. Obolensky

Abstract

The paper presents a way of constructing quasimonotone nonautonomous systems ensuring x -stability of the nonautonomous system. There are described extensions quasimonotone with respect to an arbitrary cone, Perron condition and invariant surface stability under perturbations U -stability on the set of non wandering points is proved to imply u -stability of quasimonotone nonlinear system and exponential u -stability on minimal attraction center provides u -stability of the total systems Examples are available.

Suggested Citation

  • A. A. Martynyuk & A. Yu. Obolensky, 1990. "On the theory of one-sided models in spaces with arbitrary cones," International Journal of Stochastic Analysis, Hindawi, vol. 3, pages 1-13, January.
    • Handle: RePEc:hin:jnijsa:985103
    DOI: 10.1155/S1048953390000089
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