| Autor: |
Gühring, Gabriele, Räbiger, Frank, Ruess, Wolfgang M. |
| Rok vydání: |
2000 |
| Předmět: |
|
| Zdroj: |
Differential Integral Equations 13, no. 0406 (2000), 503-527 |
| ISSN: |
0893-4983 |
| DOI: |
10.57262/die/1356061237 |
| Popis: |
We consider the semilinear non-autonomous evolution equation $\frac{d}{dt}u(t)=Au(t)+G(t,u(t))$, $t\geq s\geq 0,$ where $(A,D(A))$ is a Hille-Yosida operator on a Banach space $X$ and $G$ is a continuous function on $\mathbb R_+\times \overline{D(A)}$ with values in the extrapolated Favard class corresponding to $A$. In our main results we present principles of linearized stability and instability for a solution of such an equation. Our approach is based on the theory of extrapolation spaces. We apply the results to non-autonomous semilinear retarded differential equations. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
|
