Comparison theorems for infinite systems of parabolic functional-differential equations

Infinite Systems of Strong Parabolic Differential–functional Inequalities

We investigate a weakly coupled infinite system of nonlinear strong parabolic differential–functional inequalities of the following form (1) ∂tz (t, x) < f (t, x, z(t, x), ∂xz (t, x), ∂ xxz (t, x), z), i ∈ S, in an arbitrary domain D. The right-hand sides f i of these inequalites are functionals of an unknown function z and Volterra functionals only will be regarded in this paper. We give a fun...

Stability theorems for some functional differential equations

Asymptotics for Infinite Systems of Differential Equations

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of ordinary differential equations. In particular, we use results from ergodic theory and the asymptotic theory of C0-semigroups to obtain a characterisation, in terms of convergence of certain Cesàro averages, of those initial values which lead to convergent solutions. Moreover, we obtain estimates on the...

On the $c_{0}$-solvability of a class of infinite systems of functional-integral equations

  In this paper, an existence result for a class of infinite systems of functional-integral equations in the Banach sequence space $c_{0}$ is established via the well-known Schauder fixed-point theorem together with a criterion of compactness in the space $c_{0}$. Furthermore, we include some remarks to show the vastity of the class of infinite systems which can be covered by our result. The a...

Strong Maximum Principles for Infinite Systems of Parabolic Differential-functional Inequalities with Nonstandard Initial Inequalities

The aim of this paper is to present strong maximum principles for infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities with sums in relatively arbitrary (n+1)-dimensional time-space sets more general than the cylindrical domain.