The Liapunov Razumikhin technique is applied to obtain the uniform asymptotic stability for linear integrodifferential equations in Hilbert spaces, x′(t) = A [ x(t) + ∫ t # F (t− s)x(s)ds ] , t ≥ t0 ≥ 0, (# = 0 or −∞), which occur in viscoelasticity and in heat conduction for materials with memory.

Stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact (not ne...

In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version ofKirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.

In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scaling. We first establish uniform (in the Knudsen number) stability results in the random space for the transport equation with uncertain scattering coefficients and then prove the uniform spectral convergence (and consequently the sharp stochastic asymptotic-preserv...