Qualitative analysis of nonlinear Volterra integral equations on time scales using resolvent and Lyapunov functionals

In this paper we use the notion of the resolvent equation and Lyapunov’s method to study boundedness and integrability of the solutions of the nonlinear Volterra integral equation on time scales x(t)=a(t)−∫t0tC(t,s)G(s,x(s))Δs,t∈[t0,∞)∩T.In particular, the existence of bounded solutions with various Lp properties are studied under suitable conditions on the functions involved in the above Volterra integral equation. At the end of the paper we display some examples on different time scales.