Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces
Nonfiction, Science & Nature, Mathematics, Linear Programming, Differential Equations
| Author: | Anatoly M Samoilenko, Yuri V Teplinsky | ISBN: | 9789814434843 |
| Publisher: | World Scientific Publishing Company | Publication: | May 3, 2013 |
| Imprint: | WSPC | Language: | English |
| Author: | Anatoly M Samoilenko, Yuri V Teplinsky |
| ISBN: | 9789814434843 |
| Publisher: | World Scientific Publishing Company |
| Publication: | May 3, 2013 |
| Imprint: | WSPC |
| Language: | English |
Evolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences. For linear and nonlinear difference equations, which are defined on finite-dimensional and infinite-dimensional tori, the problem of reducibility is solved, in particular, in neighborhoods of their invariant sets, and the basics for a theory of invariant tori and bounded semi-invariant manifolds are established. Also considered are the questions on existence and approximate construction of periodic solutions for difference equations in infinite-dimensional spaces and the problem of extendibility of the solutions in degenerate cases. For nonlinear differential equations in spaces of bounded number sequences, new results are obtained in the theory of countable-point boundary-value problems.
The book contains new mathematical results that will be useful towards advances in nonlinear mechanics and theoretical physics.
Contents:
- Reducibility Problems for Difference Equations
- Invariant Tori of Difference Equations in the Space M
- Periodic Solutions of Difference Equations. Extention of Solutions
- Countable-Point Boundary-Value Problems for Nonlinear Differential Equations
Readership: Graduate students and researchers working in the field of analysis and differential equations.
Key Features:
- New theoretical results, complete with proofs
- Theory developed for equations in infinite-dimensional spaces
- Written by leading specialists in the field
Evolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences. For linear and nonlinear difference equations, which are defined on finite-dimensional and infinite-dimensional tori, the problem of reducibility is solved, in particular, in neighborhoods of their invariant sets, and the basics for a theory of invariant tori and bounded semi-invariant manifolds are established. Also considered are the questions on existence and approximate construction of periodic solutions for difference equations in infinite-dimensional spaces and the problem of extendibility of the solutions in degenerate cases. For nonlinear differential equations in spaces of bounded number sequences, new results are obtained in the theory of countable-point boundary-value problems.
The book contains new mathematical results that will be useful towards advances in nonlinear mechanics and theoretical physics.
Contents:
- Reducibility Problems for Difference Equations
- Invariant Tori of Difference Equations in the Space M
- Periodic Solutions of Difference Equations. Extention of Solutions
- Countable-Point Boundary-Value Problems for Nonlinear Differential Equations
Readership: Graduate students and researchers working in the field of analysis and differential equations.
Key Features:
- New theoretical results, complete with proofs
- Theory developed for equations in infinite-dimensional spaces
- Written by leading specialists in the field
