Properties of stationary solutions of a generalized Tjon-Wu equation

摘要

A generalized version of the Tjon-Wu equation is considered. Solutions of this equation are functions with values in the space of probability measures on [0,∞). We prove that the stationary solution μ_* of the equation has the following property: Either μ_* is supported at one point or suppμ_*=[0,∞). Moreover we show that in the second case the distribution function of μ_* is continuous. Some open questions are discussed.