Asymptotic Properties Via an Integro- differential Inequality
James Hou-fu Liu · Journal of Integral Equations and Applications · 1994
Recent results about asymptotic properties for integrodifferential equations in n are studied in Hara, et al. [6] by analyzing a Liapunov function v(•) satisfying v (t) ≤ -αv(t) + t 0 ω(t, s)v(s) ds, t ≥ t 0 ≥ 0.We will extend the techniques in [6] to the study of integrodifferential equationsin real Hilbert spaces with unbounded linear operators A(•), when a Liapunov function v(•) satisfiesThe results include uniform stability and asymptotic stability, as well as uniform boundedness and ultimate boundedness, which are not studied in [6].The above integrodifferential equations occur in viscoelasticity and in heat conduction for materials with memory.