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Exponential growth bound and exponential stability

1998
In Section 5.1, we characterize the exponential growth bound of the propagators of (ACP n ) in a Hilbert space in terms of the behavior of on vertical lines in a half complex plane. As a consequence we show that the propagators are exponentially stable if P λ is boundedly invertible in {λ ∈ C; Reλ ≥ 0} with uniformly bounded there.
Ti-Jun Xiao, Jin Liang
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Axially symmetric solutions for the planar Schrödinger-Poisson system with critical exponential growth

Journal of Differential Equations, 2020
Sitong Chen, Xianhua Tang
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Uniform Growth in Groups of Exponential Growth

Geometriae Dedicata, 2002
Let \(\Gamma\) be a group equipped with a finite system of generators \(S\) and with the corresponding word metric. The associated `growth function' is the function, defined on the set of natural numbers, which assigns to each integer \(k\geq 0\) the quantity denoted by \(\beta(\Gamma,S;k)\) which is equal to the number of elements \(\gamma\in\Gamma ...
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Exponential Growth