Exponential dichotomy and dichotomy radius for difference equations

On Exponential Dichotomy of Variational Difference Equations

Sufficient Conditions for Exponential Stability and Dichotomy of Evolution Equations

We present several suucient conditions for exponential stability and di-chotomy of solutions of the evolution equation u 0 (t) = A(t)u(t) () on a Banach space X. Our main theorem says that if the operators A(t) generate analytic semigroups on X having exponential dichotomy with uniform constants and A() has a suuciently small HH older constant, then () has exponential dichotomy. We further stud...

Roughness of (ℤ+, ℤ−)-Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces

In this paper we study the roughness of (ℤ+, ℤ-)-nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinite-dimensional spaces. An explicit form is given for each of the dichotomy constants of the perturbed equation in terms of the original ones. We emphasize that we do not assume any boundedness condition on the coefficients.

A Sufficient Condition for Exponential Dichotomy of Parabolic Evolution Equations

A dynamic dichotomy for a system of hierarchical difference equations

A system of difference equations that arises in population dynamics is studied. Criteria are given for the existence of equilibria lying in the positive cone and for the existence of periodic cycles lying on the boundary of the cone. These equilibria and cycles arise from a bifurcation that occurs as a fundamental parameter R0 increases through the value 1. Under monotone conditions on the nonl...