We consider various initial-value problems for ordinary integro-differential equations of first order that are characterized by convolution-terms, where all factors depend on the solutions of the equations. Applications of such problems are descriptions of certain glass-transition phenomena based on mode-coupling theory, for instance. We will prove results concerning well-posedness of such problems and the asymptotic behaviour of their solutions.
"On a new class of integro-differential equations." J. Integral Equations Applications 26 (4) 497 - 526, WINTER 2014. https://doi.org/10.1216/JIE-2014-26-4-497