Series:

World Scientific Series on Nonlinear Science Series A

2 primary works

Book 78

Cover of Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations
Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations.This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed.

Book 86

Cover of Elements Of Mathematical Theory Of Evolutionary Equations In Banach Spaces
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.