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Monotonicity results for non-autonomous dynamical systems: the case of a general convex cone. (English) Zbl 07630927

Summary: Let \(K\) be a closed convex cone in the state space \(\mathbb{R}^n\). This note characterizes the \(K\)-monotonicity of a non-autonomous dynamical system \(\dot x(t)=f(t,x(t))\) governed by a locally Lipschitz velocity field. We deviate from the classical literature in two important ways. Firstly, the velocity field \(f\) is not required to be differentiable with respect to the state variables. And, secondly, the closed convex cone \(K\) is allowed to be absolutely general. In particular, we impose neither pointedness, nor solidity.

MSC:

34C12 Monotone systems involving ordinary differential equations
37C60 Nonautonomous smooth dynamical systems
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