|aSamoĭlenko, A. M.|q(Anatoliĭ Mikhaĭlovich),|eauthor.
|aElements of mathematical theory of evolutionary equations in Banach spaces /|cAnatoly M. Samoilenko, National Academy of Sciences, Ukraine; Yuriy V. Teplinsky, Kamyanets-Podilsky National University, Ukraine.
|aSingapore :|bWorld Scientific,|cc2013.
|aSingapore :|aHackensack, New Jersey :|bWorld Scientific,|c
|aWorld Scientific series on nonlinear science, Series A,|x1793-1010 ;|vv. 86.
|aIncludes bibliographical references (pages 385-395) and index.
|a1. Reducibility problems for difference equations -- 2. Invariant tori of difference equations in the space M -- 3. Periodic solutions of difference equations. Extension of solutions -- 4. Countable-point boundary-value problems for nonlinear differential equations.
|aEvolutionary 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 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 -- P. 4 of cover.