Global stability of solutions of nonstationary monotone differential equations with impulsive action in the pseudolinear form

Abstract

We consider a generalization of the principle of comparison for pseudolinear differential equations with impulsive perturbations in a Banach space. On the basis of these results, we establish the conditions for the global stability in a cone of the trivial solution for the analyzed class of equations. The obtained results are used for the investigation of stability in the Takagi–Sugeno models.