In this paper, we investigate the continuous dependence of solutions of the functional dif-ferential equation with infinite delay x'(t) = f(t, x_t) on initial functions. Endowing the phasespare a g-norm as well as...In this paper, we investigate the continuous dependence of solutions of the functional dif-ferential equation with infinite delay x'(t) = f(t, x_t) on initial functions. Endowing the phasespare a g-norm as well as a supremum norm. we show that if the equation satifies a mild fadingmemory dondition, then the continuity of f in respect to the topology induced by the supremumnorm can yield the continuity of solutions of the equation in respect to the topology induced bythe g-norm which is stronger than the ahead one.展开更多
基金This research was supported in part by an NSF grant with number NSY-DMS-8521408. On leave from South China Normal University, Guangshou, PRC. This research was supported in part by the National Science Foundation of PRC
文摘In this paper, we investigate the continuous dependence of solutions of the functional dif-ferential equation with infinite delay x'(t) = f(t, x_t) on initial functions. Endowing the phasespare a g-norm as well as a supremum norm. we show that if the equation satifies a mild fadingmemory dondition, then the continuity of f in respect to the topology induced by the supremumnorm can yield the continuity of solutions of the equation in respect to the topology induced bythe g-norm which is stronger than the ahead one.
