Abstract
On considere des equations paraboliques semi-lineaires: dy/dt+Ay=f(y), ou A est un operateur sectoriel sur un Banach X ayant une resolvante compacte et f est une C 2 -application de l'espace des puissances fractionnaires Xα, 0≤α<1, dans X. Soit y(t) une solution qui est quasi convergente mais non convergente. Alors il existe un voisinage U de y 0 =y(0) avec la propriete suivante: si z∈U\{y 0 } a une trajectoire bornee et soit Z≤y 0 soit z≥y 0 , alors la solution partant de z converge vers un equilibre
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