A singular problem for functional differential equations with decreasing non-linearities

We consider a weighted initial value problem for first-order functional differential equations with monotone non-linearities which may have a non-integrable singularity with respect to the independent variable. Conditions for the existence of solutions in a suitable weighted space of locally absolutely continuous functions are given.

Automated summary

We investigate the existence of solutions in a suitable weighted space of locally absolutely continuous functions for a first-order functional differential equation with monotone non-linearities, which may have a non-integrable singularity with respect to the independent variable.