SOLUTIONS TO NONAUTONOMOUS ABSTRACT FUNCTIONAL EQUATIONS WITH INFINITE DELAY

Total Stability in Abstract Functional Differential Equations with Infinite Delay

Recently, authors [2] have discussed some equivalent relations for ρ-uniform stabilities of a given equation and those of its limiting equations by using the skew product flow constructed by quasi-processes on a general metric space. In 1992, Murakami and Yoshizawa [6] pointed out that for functional differential equations with infinite delay on a fading memory space B = B((−∞, 0];R) ρ-stabilit...

Periodic Solutions of Functional Dynamic Equations with Infinite Delay

In this paper, sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales, which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale is the set of the real numbers or the integers, respectively. The approach is mainly ba...

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Semilinear functional difference equations with infinite delay

We obtain boundness and asymptotic behavior of solutions for semilinear functional difference equations with infinite delay. Applications on Volterra difference equations with infinite delay are shown.

Regularity of Solutions to Stochastic Volterra Equations with Infinite Delay

The paper gives necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a ddimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used.