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.
