We will study ordinary integro-differential equations of second order with nonlinearity given as a convolution, but differently from the widely investigated cases. In addition, the kernel depends on the solution. Such equations play a key role in the theory of glass-forming liquids, and we will establish results on global existence and investigate the long-term behavior. In contrast, we give examples where blow-ups occur.
"Global existence and blow-Ups for certain ordinary integro-differential equations." J. Integral Equations Applications 27 (4) 573 - 602, WINTER-2015. https://doi.org/10.1216/JIE-2015-27-4-573