Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients, 1993
Mathematics and its Applications Series, Vol. 87

Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations. This volume represents an important contribution to the available methods of solution for such systems.
The contents are divided into six chapters. Chapter 1 presents a study of periodic solutions for nonlinear systems of evolution equations including differential equations with lag, systems of neutral type, various classes of nonlinear systems of integro-differential equations, etc. A numerical-analytic method for the investigation of periodic solutions of these evolution equations is presented. In Chapters 2 and 3, problems concerning the existence of periodic and quasiperiodic solutions for systems with lag are examined. For a nonlinear system with quasiperiodic coefficients and lag, the conditions under which quasiperiodic solutions exist are established. Chapter 4 is devoted to the study of invariant toroidal manifolds for various classes of systems of differential equations with quasiperiodic coefficients. Chapter 5 examines the problem concerning the reducibility of a linear system of difference equations with quasiperiodic coefficients to a linear system of difference equations with constant coefficients.
Chapter 6 contains an investigation of invariant toroidal sets for systems of difference equations with quasiperiodic coefficients.
For mathematicians whose work involves the study of oscillating systems.

Preface. 1. Numerical-Analytical Method of Investigation of Periodic Solutions for Systems with Aftereffect. 2. Investigation of Periodic Solutions of Systems with Aftereffect by Bubnov-Gelerkin's Method. 3. Quasiperiodic Solutions of Systems with Lag. Bubnov-Galerkin's Method. 4. Existence of Invariant Toroidal Manifolds for Systems with Lag. Investigation of the Behaviour of Trajectories in their Vicinities. 5. Reducibility of Linear Systems of Difference Equations with Quasiperiodic Coefficients. 6. Invariant Toroidal Sets for Systems of Difference Equations. Investigation of the Behavior of Trajectories on Toroidal Sets and in their Vicinities. References. Index.