EXISTENCE OF RESOLVENT FOR VOLTERRA INTEGRAL EQUATIONS ON TIME SCALES

DOI10.1017/S0004972709001166zbMath1198.45003OpenAlexW2101648011MaRDI QIDQ3580000

Murat Adivar, Youssef N. Raffoul

Publication date: 11 August 2010

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972709001166

zbMATH Keywords

resolventtime scalesVolterra integral equationshift operator

Mathematics Subject Classification ID

Volterra integral equations (45D05)

Related Items (24)

Convex optimization on mixed domains ⋮ Stability criteria for Volterra integrodynamic system ⋮ Estimates on some power nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales ⋮ Floquet theory for a Volterra integro-dynamic system ⋮ Volterra integral equations on time scales: stability under constant perturbations via Liapunov direct method ⋮ Weighted pseudo almost automorphic solution for abstract dynamic equations under translation and non-translation time scales with shift operators and unbounded graininess ⋮ Exponential stability of integro-differential Volterra equation on time scales ⋮ Multiple periodic solutions in shifts \(\delta_{\pm}\) for an impulsive functional dynamic equation on time scales ⋮ Functional Volterra Stieltjes integral equations and applications ⋮ Boundedness and stability in nonlinear systems of differential equations using a modified variation of parameters formula ⋮ Absolute continuity and existence of solutions to dynamic inclusions in time scales ⋮ Halanay type inequalities on time scales with applications ⋮ Periodic solutions in shifts \(\delta_\pm\) for a nonlinear dynamic equation on time scales ⋮ Complete-closed time scales under shifts and related functions ⋮ Controllability, observability, and stability of a Volterra integro-dynamic system on time scales ⋮ Stability and convergence of solutions to Volterra integral equations on time scales ⋮ Positive periodic solutions in shifts \(\delta_\pm\) for a class of higher-dimensional functional dynamic equations with impulses on time scales ⋮ Qualitative analysis of nonlinear Volterra integral equations on time scales using resolvent and Lyapunov functionals ⋮ Floquet theory based on new periodicity concept for hybrid systems involving \(q\)-difference equations ⋮ Volterra theory on time scales ⋮ n₀-order Δ-almost periodic functions and dynamic equations ⋮ Recent results on summations and Volterra difference equations via Lyapunov functionals ⋮ PRINCIPAL MATRIX SOLUTIONS AND VARIATION OF PARAMETERS FOR VOLTERRA INTEGRO-DYNAMIC EQUATIONS ON TIME SCALES ⋮ On Volterra integral equations on time scales

Cites Work

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• Analysis on measure chains - a unified approach to continuous and discrete calculus
• Basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling
• Double integral calculus of variations on time scales
• The exponential of a constant matrix on time scales
• Oscillation of symplectic dynamic systems

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