The author studies the existence of a nontrivial (nonzero) solution to the equation \[ u(x) = \int_0^x k(x-s)g(u(s)) ds, \] where \(k\) is integrable and positive, and \(g\) is continuous, strictly increasing with \(g(0)=0\), the set \(\{x\geq 0\mid g'(x)=0\}\) has measure zero and \(g\) transforms sets of measure zero into such sets. It is shown that there is a nontrivial solution if and only if there is a positive measurable function \(f\) such that \(\int_0^x K(\int_s^x f(r) dr) ds \geq g^{-1}(x)\) where \(K(x)=\int_0^x k(s) ds\). The uniqueness of such increasing solutions is also established.