Stability of solutions of linear systems with dominant main diagonal
Charles S. Kahane · Proceedings of the American Mathematical Society · 1972
We establish the asymptotic stability of solutions of a first order linear system of differential equations in which the matrix characterizing the system has a dominating principal diagonal with negative entries; the domination is expressed through the condition that, numerically, each entry in the principal diagonal exceeds the sum of the absolute values of the remaining entries in the same column.