ON THE UNBOUNDED BEHAVIOR FOR SOME NONAUTONOMOUS SYSTEMS IN BANACH-SPACES

[摘要] By modifying our previous methods (1992, J. Nonlinear AnaL TMA 19, 741-751; 1993, Proc. Amer. Math. Soc. 117, 951-956), and by using the notion of integral solution introduced by Ph. Benilan (1972, ''Equations d'evolution dans un espace de Banach quelconque et applications,'' thesis, Universite Paris XI, Orsay), we study the asymptotic behaviour of unbounded trajectories for the quasi-autonomous dissipative system du/dt + Au contains f where X is a real Banach space, A an accretive (possibly multivalued) operator in X x X, and f-f(infinity) is-an-element-of L(p)((0, + infinity); X) for some f(infinity) is-an-element-of X and 1 less-than-or-equal-to p < infinity. (C) 1994 Academic Press, Inc.

[发布日期] 1994-06-01