Abstract
Nonlinear nonautonomous evolution equations in a space with a normalizing mapping (a generalized norm) are considered. Solution estimates are established. In particular cases these estimates generalize the Wazewski and Lozinskii estimates from the theory of ordinary differential equations. By the obtained estimates, the following problems are investigated: asymptotic stability, boundedness of solutions, input-output stability, existence of periodic solutions. Applications to integro-differential equations are discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 1-23 |
| Number of pages | 23 |
| Journal | Acta Applicandae Mathematicae |
| Volume | 69 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Oct 2001 |
Keywords
- Asymptotic stability
- Boundedness of solutions
- Input-output stability
- Integro-differential equations
- Nonlinear evolution equations
- Periodic solutions
ASJC Scopus subject areas
- Applied Mathematics
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