Geodesic
Equivalence of Lp Stability and Exponential Stability of Nonlinear Lipschitzian Semigroups
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 882-889

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DOI

${{L}_{p}}$ stability and exponential stability are two important concepts for nonlinear dynamic systems. In this paper, we prove that a nonlinear exponentially bounded Lipschitzian semigroup is exponentially stable if and only if the semigroup is ${{L}_{p}}$ stable for some $p\,>\,0$ . Based on the equivalence, we derive two sufficient conditions for exponential stability of the nonlinear semigroup. The results obtained extend and improve some existing ones.
DOI : 10.4153/CMB-2011-070-0
Mots-clés : 34D05, 47H20, exponentially stable, Lp stable, nonlinear Lipschitzian semigroups 
Xueli, Song; Jigen, Peng. Equivalence of Lp Stability and Exponential Stability of Nonlinear Lipschitzian Semigroups. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 882-889. doi: 10.4153/CMB-2011-070-0
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     author = {Xueli, Song and Jigen, Peng},
     title = {Equivalence of {Lp} {Stability} and {Exponential} {Stability} of {Nonlinear} {Lipschitzian} {Semigroups}},
     journal = {Canadian mathematical bulletin},
     pages = {882--889},
     year = {2012},
     volume = {55},
     number = {4},
     doi = {10.4153/CMB-2011-070-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-070-0/}
}
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