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Integro-differential equations on time scales with Henstock-Kurzweil delta integrals

Aneta Sikorska-Nowak (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we prove existence theorems for integro - differential equations x Δ ( t ) = f ( t , x ( t ) , t k ( t , s , x ( s ) ) Δ s ) , t ∈ Iₐ = [0,a] ∩ T, a ∈ R₊, x(0) = x₀ where T denotes a time scale (nonempty closed subset of real numbers R), Iₐ is a time scale interval. Functions f,k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral. Additionally, functions f and k satisfy some boundary conditions and conditions...

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