Positive and Monotone Systems in a Partially Ordered Space
Copyright policy )Positive and Monotone Systems in a Partially Ordered Space
The author considers the equation \[ X'(t)+M(t)X(t)=G(t),\tag{1} \] where \(M(t)\), for each \(t\geq 0\), is a bounded operator on a Banach space with a cone. Under some monotonicity conditions (close to the necessary ones) the dynamical system described by the equation (1) is shown to be positive and exponentially stable. Using comparison and perturbation methods the author finds also sufficient conditions for asymptotic stability.
- National Academy of Sciences of Ukraine Ukraine
- Polish Academy of Sciences Poland
- Institute of Mathematics Poland
Banach space with a cone, asymptotic stability, Linear differential equations in abstract spaces, exponential stability, Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems, Linear operators on ordered spaces, Stability of solutions to ordinary differential equations, dynamical system
Banach space with a cone, asymptotic stability, Linear differential equations in abstract spaces, exponential stability, Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems, Linear operators on ordered spaces, Stability of solutions to ordinary differential equations, dynamical system
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