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Title Topics on stability and periodicity in abstract differential equations / James H. Liu, Gaston M. N'Guérékata, Nguyen Van Minh.
Imprint Singapore : World Scientific, ©2008.


 Internet  Electronic Book    AVAILABLE
Description 1 online resource (ix, 208 pages) : illustrations
Series Series on concrete and applicable mathematics ; v. 6
Series on concrete and applicable mathematics ; v. 6.
Bibliog. Includes bibliographical references and index.
Note Available only to authorized UTEP users.
Print version record.
Subject Differential equations -- Asymptotic theory.
Genre Electronic books.
Contents 1. Preliminaries. 1.1. Banach spaces and linear operators. 1.2. Strongly continuous semigroups of operators. 1.3. Spectral theory -- 2. Stability and exponential dichotomy. 2.1. Perron theorem. 2.2. Evolution semigroups and Perron theorem. 2.3. Stability theory. 2.4. Comments and further reading guide -- 3. Almost periodic solutions. 3.1. Evolution semigroups & periodic equations. 3.2. Sums of commuting operators. 3.3. Decomposition theorem. 3.4. Comments and further reading guide -- 4. Almost automorphic solutions. 4.1. The inhomogeneous linear equation. 4.2. Method of invariant subspaces and almost automorphic solutions of second-order differential equations. 4.3. Existence of almost automorphic solutions to semilinear differential equations. 4.4. Method of sums of commuting operators and almost automorphic functions. 4.5. Almost automorphic solutions of second order evolution equations. 4.6. The equations x'=f(t, x). 4.7. Comments and further reading guide -- 5. Nonlinear equations. 5.1. Periodic solutions of nonlinear equations. 5.2. Evolution semigroups and almost periodic solutions. 5.3. Comments and further reading guide.
Summary This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas.
Other Author N'Guerekata, Gaston M., 1953-
Minh, Nguyen Van.
Other Title Print version: Liu, James Hetao. Topics on stability and periodicity in abstract differential equations. Singapore : World Scientific, ©2008