The qualitative behavior of a nonlinear Volterra equation

Abstract

has been studied under various assumptions on the given functions b(t), f(t), g(x). A large literature exists for the particular case of (1.1), called the renewal equation, where b(t) ?0 ?f(t) and g(x) x; see [i] for references. Motivated by certain problems in heat transfer and superfluidity, the special case of (1.1) where b(t) = t-112, f(t) is periodic, and g(x) is monotone increasing with g(O) =0 has been investigated in [3], [4], [6], [8]. (Except in [3], f(t)-1. In [8], b(t) EEL1(0, oo) is taken more generally than b(t) = t-112.) The equation