Abstract
On etudie l'equation operateur BA 1 u+A 0 u=h dans des espaces de Banach sous certaines hypotheses permettant d'appliquer les resultats obtenus pour le probleme aux valeurs initiales d(A 1 (t)u(t)/dt+A 0 (t)u(t)=h(t), 0<t≤T<+∞, lim t→0 A 1 (t)u(t)=0, ou A i (t), (i=0,1), est un bon operateur lineaire clos entre espaces de Banach
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