Exponential stability and instability in nonlinear differential equation with multiple delays

• Afful, Adusei-Poku ^[1] ; Yankson, Ernest ^[1]
  1. [1] University of Cape Coast

     University of Cape Coast

     Ghana

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 3, 2023, págs. 681-693
• Idioma: inglés
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• Resumen

  • 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.