Sufficient condition for the existence of a solution to the equation of nonlocal ionization source in a glow discharge

A sufficient condition for the existence of a solution to the Gorin integral equation for a nonlocal source of ionization in a dc glow discharge of an arbitrary geometry, including a hollow-cathode glow discharge, is formulated and proved. Together with the theorem of uniqueness of solution, stated and proved earlier, this provides reliable mathematical basics for simulating nonlocal phenomena using convenient physically meaningful structures.