ASYMPTOTICS AND STABILITY OF NONLINEAR PARAMETRIC OSCILLATIONS OF A SINGULARLY PERTURBED TELEGRAPH EQUATION

The solution of the problem indicated in the title is based on the met hod of quasi-normal forms developed previously by the author for the c onstruction of stationary regimes of parabolic systems with small diff usion. As in the parabolic case, it relies on the theory of exponentia l dichotomy of solutions and on an algorithm in the study of stability of linear differential equations whose coefficients are nearly indepe ndent of the time.