| Full text | |
| Author(s): |
Aragao Costa, Eder Ritas
Total Authors: 1
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| Document type: | Journal article |
| Source: | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS; v. 18, n. 2, p. 845-868, MAR 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper we prove versions, in Frechet spaces, of the classical theorems related to exponential dichotomy for a sequence of continuous linear operators on Banach spaces. To be more specific, here we define a kind of exponential dichotomy in Frechet spaces, which extends the former one in Banach spaces, establish necessary conditions for its existence and provide sufficient conditions for its stability under perturbation. We apply the conclusions by providing an example of a semigroup of bounded linear operators, on a Frechet space, which has this new exponential dichotomy but does not in Banach spaces, namely, [e(m Delta) : m epsilon N], where Delta is the Laplace operator on the unbounded domain R-n \textbackslash{}[0]. Also, we show how these new concepts allow us to study a hyperbolic equilibrium point of a backwards heat equation with nonlinearity involving convolution products, which cannot be obtained from the knowledge of exponential dichotomy in Banach spaces. (AU) | |
| FAPESP's process: | 14/02899-3 - Global solvability for differential complexes and converse to the theorem of the existence of Lyapunov function to gradient-like evolution process |
| Grantee: | Éder Ritis Aragão Costa |
| Support Opportunities: | Regular Research Grants |