Anatoliy M Samoilenko's Books

Numerical-analytic Methods In Theory Of Boundary- Value Problems

By: Miklos Ronto,Anatoliy M Samoilenko

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Numerical-analytic Methods In Theory Of Boundary- Value Problems

By: Miklos Ronto,Anatoliy M Samoilenko

This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs.The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari-Hale and Lyapunov-Schmidt methods.

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467

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World Scientific

Published Date

ISBN 10

9814495484

ISBN 13

9789814495486

Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations

By: Anatoliy M. Samoilenko,Oleksandr Stanzhytskyi

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Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations

By: Anatoliy M. Samoilenko,Oleksandr Stanzhytskyi

1. Differential equations with random right-hand sides and impulsive effects. 1.1. An impulsive process as a solution of an impulsive system. 1.2. Dissipativity. 1.3. Stability and Lyapunov functions. 1.4. Stability of systems with permanently acting random perturbations. 1.5. Solutions periodic in the restricted sense. 1.6. Periodic solutions of systems with small perturbations. 1.7. Periodic solutions of linear impulsive systems. 1.8. Weakly nonlinear systems. 1.9. Comments and references -- 2. Invariant sets for systems with random perturbations. 2.1. Invariant sets for systems with random right-hand sides. 2.2. Invariant sets for stochastic Ito systems. 2.3. The behaviour of invariant sets under small perturbations. 2.4. A study of stability of an equilibrium via the reduction principle for systems with regular random perturbations. 2.5. Stability of an equilibrium and the reduction principle for Ito type systems. 2.6. A study of stability of the invariant set via the reduction principle. Regular perturbations. 2.7. Stability of invariant sets and the reduction principle for Ito type systems. 2.8. Comments and references -- 3. Linear and quasilinear stochastic Ito systems. 3.1. Mean square exponential dichotomy. 3.2. A study of dichotomy in terms of quadratic forms. 3.3. Linear system solutions that are mean square bounded on the semiaxis. 3.4. Quasilinear systems. 3.5. Linear system solutions that are probability bounded on the axis. A generalized notion of a solution. 3.6. Asymptotic equivalence of linear systems. 3.7. Conditions for asymptotic equivalence of nonlinear systems. 3.8. Comments and references -- 4. Extensions of Ito systems on a torus. 4.1. Stability of invariant tori. 4.2. Random invariant tori for linear extensions. 4.3. Smoothness of invariant tori. 4.4. Random invariant tori for nonlinear extensions. 4.5. An ergodic theorem for a class of stochastic systems having a toroidal manifold. 4.6. Comments and references -- 5. The averaging method for equations with random perturbations. 5.1. A substantiation of the averaging method for systems with impulsive effect. 5.2. Asymptotics of normalized deviations of averaged solutions. 5.3. Applications to the theory of nonlinear oscillations. 5.4. Averaging for systems with impulsive effects at random times. 5.5. The second theorem of M.M. Bogolyubov for systems with regular random perturbations. 5.6. Averaging for stochastic Ito systems. An asymptotically finite interval. 5.7. Averaging on the semiaxis. 5.8. The averaging method and two-sided bounded solutions of Ito systems. 5.9. Comments and references

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323

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World Scientific

Published Date

ISBN 10

981432907X

ISBN 13

9789814329071

Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces

By: Anatoliy M Samoilenko,Yuriy Teplinsky

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Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces

By: Anatoliy M Samoilenko,Yuriy Teplinsky

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.

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408

Publisher

World Scientific

Published Date

ISBN 10

9814434841

ISBN 13

9789814434843

Impulsive Differential Equations

By: N Perestyuk,Anatoliy M Samoilenko

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Impulsive Differential Equations

By: N Perestyuk,Anatoliy M Samoilenko

Contents:General Description of Impulsive Differential SystemsLinear SystemsStability of SolutionsPeriodic and Almost Periodic Impulsive SystemsIntegral Sets of Impulsive SystemsOptimum Control in Impulsive SystemsAsymptotic Study of Oscillations in Impulsive SystemsA Periodic and Almost Periodic Impulsive SystemsBibliographySubject Index Readership: Researchers in nonlinear science. keywords:Differential Equations with Impulses;Linear Systems;Stability;Periodic and Quasi-Periodic Solutions;Integral Sets;Optimal Control “… lucid … the book … will benefit all who are interested in IDE…” Mathematics Abstracts

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474

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World Scientific

Published Date

ISBN 10

981449982X

ISBN 13

9789814499828

Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces

By: Anatoliy M Samoilenko,Yuriy Teplinsky

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Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces

By: Anatoliy M Samoilenko,Yuriy Teplinsky

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Solve jigsaw puzzle

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Page Count

408

Publisher

World Scientific

Published Date

ISBN 10

9814434841

ISBN 13

9789814434843

Book's by Anatoliy M Samoilenko

Numerical-analytic Methods In Theory Of Boundary- Value Problems

Numerical-analytic Methods In Theory Of Boundary- Value Problems

Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations

Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations

Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces

Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces

Impulsive Differential Equations

Impulsive Differential Equations

Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces

Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces

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