Existence of asymptotically almost periodic solutions of integrodifferential equations

In this paper, a class of semilinear integrodifferential equations of the formu′′(t) +αu′′′(t) =βAu(t) +γAu′(t) +f(t, u(t)) +∫t0g(t, s, u(s))ds, t, s≥0,satisfyingαβ < γwith prescribed initial conditions are studied. Using certain strongly continuousfamilies in operator theory and fixed point theory, we have established some sufficient con-ditions for the existence and uniqueness of an asymptotically almost periodic solutions