A norm estimate for evolution operators of equations with the Lipschitz property in a Banach space
Michael Gil'
Ben Gurion University of the Negev, Beer-Sheva, Israel
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Abstract
In a Banach space we consider the equation , where is a constant operator, generating a -semigroup, and is a bounded variable operator with the Lipschitz property. A norm estimate for the evolution operator of the considered equation is established. That estimate gives us exponential stability conditions. An illustrative example is given.
Cite this article
Michael Gil', A norm estimate for evolution operators of equations with the Lipschitz property in a Banach space. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 1, pp. 169–174
DOI 10.4171/RLM/840