Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals

We prove existence theorems for integro-differential equations Δ∫()=(,(),0(,,())Δ), (0)=0, ∈=[0,]∩, ∈+, where denotes a time scale (nonempty closed subset of real numbers ), and is a time scale interval. The functions , are weakly-weakly sequentially continuous with values in a Banach space , and the integral is taken in the sense of Henstock-Kurzweil-Pettis delta integral. This integral generalizes the Henstock-Kurzweil delta integral and the Pettis integral. Additionally, the functions and satisfy some boundary conditions and conditions expressed in terms of measures of weak noncompactness. Moreover, we prove Ambrosetti's lemma