SINGULAR PERTURBATION ANALYSIS OF BOUNDARY-VALUE-PROBLEMS FOR DIFFERENTIAL-DIFFERENCE EQUATIONS .2. RAPID OSCILLATIONS AND RESONANCES

This paper continues a study of a class of boundary-value problems for linear second-order differential-difference equations in which the second-order derivative is multiplied by a small parameter. The previous paper focused on problems involving boundary and interior layer phenomena. Here the problems studied have solutions exhibiting rapid oscillations. The presence of the shift terms can induce large amplitudes, multiphase behavior, and resonance phemonena. In particular, we study two types of resonance amplitudes, multiphase behavior, and resonance phenomena. In particular, we study two types of resonance phenomena, namely 'global' and 'local' resonance. A combination of exact solutions, singular perturbation methods, and numerical computations are used in these studies.