Theorem on the existence of two-point oscillatory solutions to a relay perturbed system with a negative eigenvalue of the matrix

Аннотация

We consider an $n$-dimensional system of ordinary first-order differential equations with a nonlinearity of a non-ideal relay and a continuous periodic function of perturbation in the right-hand side. The system matrix has simple, real, nonzero eigenvalues and at least one is negative. We study continuous oscillatory solutions with two switching points in phase space and with the same time of return to each of these points on the discontinuity surface. The theorem of the existence of the solution and its parameters are established. An example illustrating the obtained results is given.