Sufficient Conditions for the Stability of Trivial Solutions of a Certain Class of Nonlinear Delay Differential Equations
Keywords:Stability, Trivial solution, nonlinear delay differential equations, (DDES) Perturbation, linear and homogeneous system
AbstractIn thisÂ paper Â we study Â the stability of a trivial solution of Â certain Â nonlinear delay differential equations of the form where for us to improves on the existence literature, equation (1.1) was re-written as a perturbation of the linear homogeneous system of the form and and we use existences an uniqueness theorem of a linear system to establish sufficient conditions that guarantee the stability of the trivial solutions of a certain class of nonlinear delay differential equations. The goal of this paper is to give a simple criterion for the stability of (1.1) when re-written as a perturbation of a linear homogeneous system of the form (1.3) and (1.4).
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