Exponential stability and instability in nonlinear differential equation with multiple delays
DOI:
https://doi.org/10.22199/issn.0717-6279-4197Keywords:
exponential stability, Lyapunov functional, instabilityAbstract
Inequalities regarding the solutions of the nonlinear differential equation with multiple delays
xl(t) = a(t)f(x(t)) +Σni=1bi(t)f(x(t − hi)),
are obtained by means of Lyapunov functionals. These inequalities are then used to obtain sufficient conditions that guarantee exponential decay of solutions to zero of the multi delay nonlinear differential equation. In addition, we obtain a criterion for the instability of the zero solution. The results generalizes some results in the literature.
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