Boundary-value problems with parameters for a multifrequency oscillation system

Abstract

By using the averaging method, we prove the solvability of boundary-value problems with parameters for nonlinear oscillation systems. We obtain estimates for the deviation of solutions of averaged problems from solutions of original problems. UDC 517.9We consider the following nonlinear system of ordinary differential equations:Its right-hand side is defined for (x, qo, % e)E D x R m x [0, L] x (0, e0] (here, eo << 1, D is a bounded domain of the real Euclidean space R~). We may take the functions a and b to have bounded continuous partial derivatives with respect to x, % and "c up to thesecond order and to be almost periodic in qo v, v = 1, m. We also assume that