Quasi-periodic Solutions of Nonlinear Ordinary Differential Equations with Small Damping
نویسنده
چکیده
f(t) = Ffaxt, ù)2t, • • • , COmt) where F(0it • • • , 0m) is a continuous function of period 2T in 0V1 v = 1, • • • , m. The numbers wi, • • • , œm are called the basic frequencies of ƒ(/). We shall denote by Afai, • • • , o)m) the class of all functions ƒ for which F is real analytic. For simplicity of notation we set 0=(0i, • • • , 0m) and w=(coi, • • • , o)m) (then i4(a>i, • • • , com)=4(w) and F(0X, • • • ,ftn) = F(0)). The purpose of this note is to study the family of complex systems of differential equations:
منابع مشابه
ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS
Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...
متن کاملQuasi-periodic motions in strongly dissipative forced systems
We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasi-periodic solutions which have the same frequency vector as the forcing.
متن کاملSummation of divergent series and Borel summability for strongly dissipative equations with periodic or quasi-periodic forcing terms
We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasi-periodic analytic forcing term and in the presence of damping. As a physical application one can think of a resistorinductor-varactor circuit with a periodic (or quasi-periodic) forcing function, even if the range of applicability of the theory is much wider. In the limit of large...
متن کاملConstruction of quasi-periodic response solutions in forced strongly dissipative systems
We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is quasi-periodic solutions which have the same frequency vector as the forcing. This requires dealing with a degenerate implicit function equation: we prove that the l...
متن کاملDhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations
In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...
متن کامل