An asymptotic theory for retarded functional difference equations

Heteroclinic Orbits for Retarded Functional Differential Equations*

Suppose r is a heteroclinic orbit of a Ck functional differential equation i(t) =f(x,) with a-limit set a(T) and o-limit set w(T) being either hyperbolic equilibrium points or periodic orbits. Necessary and sufficient conditions are given for the existence of an 7 close to f in Ck with the property that i(t) = 3(x,) has a heteroclinic orbit p close to f. The orbits p are obtained from the zeros...

Asymptotic behavior for retarded parabolic equations with superlinear perturbations

We obtain the existence and uniqueness of solutions for a class of retarded parabolic equations with superlinear perturbations. The asymptotic behavior result is studied by using the pullback attractor framework.

Asymptotic Properties for Half-linear Difference Equations

Dedicated to Prof. Jaroslav Kurzweil on the occasion of his 80th birthday Abstract. Asymptotic properties of the half-linear difference equation (∗) ∆(an|∆xn| α sgn∆xn) = bn|xn+1| α sgnxn+1 are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to (∗) are considered too. Our approach is based on a classification of solutions of (...

Asymptotic Analysis for Linear Difference Equations

We are concerned with asymptotic analysis for linear difference equations in a locally convex space. First we introduce the profile operator, which plays a central role in analyzing the asymptotic behaviors of the solutions. Then factorial asymptotic expansions for the solutions are given quite explicitly. Finally we obtain Gevrey estimates for the solutions. In a forthcoming paper we will deve...

Existence of Periodic and Almost Periodic Solutions of Abstract Retarded Functional Difference Equations in Phase Spaces