On the robust stability of stationary solutions to a class of Mathieu-type equations

Abstract

We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equation under which the zero solution is asymptotically stable. Estimates for attraction sets of the zero solution and estimates of the stabilization rate of solutions at infinity are obtained. Using these results, theorems on the robust stability of stationary solutions are proven.