Structural properties of the implicit function defined by an integral self-consistency equation

Ivan Viakhirev

We study the integral equation ${\int }_0^m\eta \rho (\eta )/(C-\eta )d\eta =1$ with $C>m$, where $\rho$ is a $C^1$ probability density on $[0,M]$ vanishing polynomially at $\eta =M$. Setting $\mathcal{I}^+…