On Exponential Dichotomy of Variational Difference Equations
نویسندگان
چکیده
منابع مشابه
On Dichotomous Behavior of Variational Difference Equations and Applications
We give new and very general characterizations for uniform exponential dichotomy of variational difference equations in terms of the admissibility of pairs of sequence spaces over N with respect to an associated control system. We establish in the variational case the connections between the admissibility of certain pairs of sequence spaces over N and the admissibility of the corresponding pair...
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For a sequence of bounded linear operators {An}n=0 on a Banach space X , we investigate the characterization of exponential dichotomy of the difference equations vn+1 = Anvn. We characterize the exponential dichotomy of difference equations in terms of the existence of solutions to the equations vn+1 = Anvn + fn in lp spaces (1 ≤ p <∞). Then we apply the results to study the robustness of expon...
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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.
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MIHAELA AURELIA TOMESCU University of Petroşani Department of Mathematics and Computer Science University Street 20, 332006 Petroşani ROMANIA [email protected] MIHAIL MEGAN Academy of Romanian Scientists Independenţei 54, 050094 Bucharest ROMANIA West University of Timişoara Department of Mathematics V. Pârvan Blv. No. 4, 300223 Timişoara ROMANIA [email protected] TRAIAN CEAUŞU West University o...
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This paper deals with two concepts of polynomial dichotomy for linear difference equations which are defined in a Banach space and whose norms can increase not faster than exponentially. Some illustrating examples clarify the relations between these concepts. Our approach is based on the extension of techniques for exponential dichotomy to the case of polynomial dichotomy. The obtained results ...
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