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    Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces

    ISBN-10: 9814434825
    ISBN-13: 9789814434829
    Author(s): Anatoly M. Samoilenko, Yuri V. Teplinsky
    Description: 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  More...
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    Publisher: World Scientific Publishing Co Pte Ltd
    Binding: Hardcover
    Pages: 397
    Size: 6.25" wide x 9.25" long x 1.25" tall
    Weight: 1.540
    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.

    Preface
    Reducibility problems for difference equations
    On analogs of the Erugin and Floquet-Lyapunov theorems for equations in the space m
    Linear equations in the space m defined on tori
    Nonlinear almost periodic equations denned on an infinite-dimensional torus
    Reduction of a discrete dynamical system in the space R<sup>q</sup> to the canonical form in a neighborhood of its invariant set
    Investigation of a discrete dynamical system defined in an abstract Banach space in a neighborhood of its invariant set
    Invariant tori of difference equations in the space m
    Sufficient conditions of existence of a continuous invariant torus
    On the differentiability of an invariant torus with respect to the angular variable and the parameter in the coordinate-wise meaning
    Truncation method in studying the smoothness of invariant tori
    Case of linear and quasilinear systems defined on the infinite-dimensional tori
    On the existence of the invariant tori of nonlinear systems
    Differentiability of the invariant tori of nonlinear systems in the Fr�chet meaning
    Conditions of existence of the Green-Samoilenko function for a linear system defined on the set m � T<sub>&#8734;</sub> Reduction of the problem of construction of the invariant torus of this system to an analogous problem in the space R<sup>s</sup> � T<sub>m</sub>
    On the existence of the smooth bounded semi-invariant manifold of a degenerate nonlinear system
    Periodic solutions of difference equations. Extension of solutions
    On the periodic solutions of linear and quasilinear equations with periodic coefficients in the space m
    Periodic solutions of nonlinear difference equations of the first order in an abstract Banach space
    Periodic solutions of nonlinear difference equations of the second order
    Asymptotic periodicity of solutions of a linear equation in a complex Banach space
    Extension "to the left" of solutions of nonlinear degenerate difference equations
    Countable-point boundary-value problems for nonlinear differential equations
    Boundary-value problem on the semiaxis
    Boundary-value problems on an interval
    Reduction to a finite-dimensional multipoint case
    Another means of the reduction. Conditions of commutativity of the limiting transitions (4.42) and (4.43)
    Boundary-value problems for differential equations unsolvable with respect to the derivative
    Reduction to a finite-dimensional multipoint problem
    Bibliography
    Index

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