Bøger af Anatoliy M (Nat'l Academy Of Sci Of Ukraine Samoilenko

For researchers in nonlinear science, this work includes coverage of linear systems, stability of solutions, periodic and almost periodic impulsive systems, integral sets of impulsive systems, optimal control in impulsive systems, and more.

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 the random factors. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations.

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.