On the Unbounded Behavior for Some Non-autonomous Systems in Banach Spaces

AbstractBy modifying our previous methods (1992, J. Nonlinear Anal TMA19, 741-751; 1993, Proc. Amer. Math. Soc.117, 951-956), and by using the notion of integral solution introduced by Ph. Bénilan (1972, "Equations d′évolution dans un espace de Banach quelconque et applications," thesis, Université Paris XI, Orsay), we study the asymptotic behaviour of unbounded trajectories for the quasi-autonomous dissipative system du/dt + Au ∋ ƒ where X is a real Banach space, A an accretive (possibly multivalued) operator in X × X, and ƒ − ƒ∞ ∈ Lp((0, + ∞); X) for some ƒ(∞) ∈ X and 1 ≤ p < ∞