Behavior of Solutions of Nonlinear Functional Volterra Integro-Differential Equations With Multiple Delays

Abstract

The authors consider the nonlinear functional Volterra integro-differential equation with multiple delays x'(t) = -a(t)x(t) + Sigma(n)(i=1) integral(t)(t-tau i) b(i)(t,s)f(i)(x(s))ds. They give sufficient conditions so that solutions are bounded, belong to L-1, or belong to L-2. They also prove the stability and global asymptotic stability of the zero solution. Their technique of proof involves defining appropriate Lyapunov functionals.