We prove existence theorems for integro-differential equations , , , , 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.
Aneta Sikorska-Nowak. "Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals." Abstr. Appl. Anal. 2010 1 - 17, 2010. https://doi.org/10.1155/2010/836347