STABILITY AND ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Itiswellknownthattheexistenceofalmostperiodicsolutionsiscloselyrelatedtothestabilityofsolutions.Forfunctionaldifferentialequationswithinfinitedelay,Y.Hin.5'6]studiedtheproblemsontheexistenceofalmostperiodicsolutionsandthestability.However,therearefewpapersll2]dealingwithneutralfunctionaldifferentialequationswithinfinitedelay.Inthepresentpaper,forneutralfunctionaldifferentialequationswithinfinitedelay,weprovetheinherencetheoremfortheuniformlystableoperatorD(t),definethestabilitywithrespecttot…

Stability and almost periodic solutions of neutral functional differential equations with infinite delay

For the operatorD(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect toH _D,f ⁺ (ξ), then Eq.(1) has anmω-periodic solutionp(t), for some integerm ≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance fromH ⁺(ξ,D,f), then Eq.(1) has an almost periodic solution. This work is supported by the National Natural Science Foundation of China.