Existence of a solution and averaging of nonlinear multifrequency problems with delay
The method of averaging over the fast variables is applied to the investigation of multifrequency systems with linearly transformed argument. We prove the existence of solutions of the initial-and boundary-value problems in a small neighborhood of the solution of the averaged problem and estimate the error of the method of averaging for slow variables.
English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 4, pp 485-499.
Citation Example: Bigun Ya. I. Existence of a solution and averaging of nonlinear multifrequency problems with delay // Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 435–446.