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A note on global asymptotic stability of nonautonomous master equations

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  • We present sufficient conditions to either preclude or guarantee global asymptotic stability of linear differential equations for time-dependent $\mathbb W$-matrices. These conditions are concerned with integrability or non-integrability of the matrix entries. The proofs employ differential inequalities.
    Mathematics Subject Classification: Primary: 34D05, 34D23; Secondary: 37B55.


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  • [1]

    A. Berman and R. J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences," Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979.


    B. A. Earnshaw and J. P. Keener, Global asymptotic stability of solutions of nonautonomous master equations, SIAM J. Applied Dynamical Systems, 9 (2010), 220-237.doi: 10.1137/090763421.


    N. G. van Kampen, "Stochastic Processes in Physics and Chemistry," Lecture Notes in Mathematics, 888, North-Holland Publishing Co., Amsterdam-New York, 1981.


    W. Walter, "Gewöhnliche Differentialgleichungen," 7. Aufl., Springer-Verlag, Berlin, 2000.

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