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.

So far there are not many results on the stability for stochastic functional differential equations with infinite delay. Themain aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay ...

In 2013, Tommi Lehtinen and Alexander Okhotin proved that if X is a code, then it has infinite deciphering delay if and only if there exist + ∈ A z y x , , with * , , , X zy yz xy x ∈ and * , X z y ∉ . In this paper, we give a sufficient and necessary condition for codes with infinite deciphering delay. Then, we construct two kinds of three-element codes with infinite deciphering delay.