Exponential Stability and Instability in Multiple Finite Delay Volterra Integro-Differential Equations

Abstract

In this thesis, sufficient conditions that guarantee the exponential stability and also instability of the zero solution of a certain class of Volterra integro-differential equations with multiple finite delays are obtained.Two Lyapunov functionals are constructed in the thesis. These Lyapunov functionals are used to obtain in- equalities that the solutions of the Volterra integro-differential equations satisfy. These inequalities are used to deduce exponential stability results for thezero solution oftheVolterraintegro-differential equations,as well as a criteria for instability ofthezerosolutionoftheVolterraintegro-differential equations.