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Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential
On the asymptotic behavior of an exponentially bounded, strongly continuous cocycle over a semiflow
1. | Department of Mathematics, University of California, Los Angeles, CA 90095 |
2. | Department of Mathematics, West University of Timişoara, Timişoara 300223, Romania, Romania |
$||\Phi(\theta, \tau_{\theta,x})x|| \leq c||x||.$
As a consequence of the above result we obtain generalizations, in both continuous-time and discrete-time, of the the well-known theorems of Datko-Pazy, Rolewicz and Zabczyk for an exponentially bounded, strongly continuous cocycle over a semiflow $\sigma$. A version of the above theorems for the case of the exponential instability is also obtained.
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