Uniform decay estimates for solutions of a class of retarded integral inequalities

Some uniform decay estimates are established for solutions of the following type retarded integral inequalities:y(t)?E(t,?)?y??+??tK1(t,s)?ys?ds+?t?K2(t,s)?ys?ds+?,t???0. As a simple example application, scalar functional differential equation x?=?a(t)x+B(t,xt) is considered, and global asymptotic stability proved under weaker conditions. Another ODE system x?=F0(t,x)+?i=1mFi(t,x(t?ri(t))) on Rn with superlinear nonlinearities Fi (0?i?m). The existence pullback attractor appropriate dissipation third application concerns study dynamics cocycle dudt+Au=F(?tp,ut) in Banach space X sublinear nonlinearity. In particular, uniqueness nonautonomous equilibrium solution ? obtained hyperbolicity assumption operator A some additional hypotheses, also addressed.