  Systems of the form $x = (A x^s)^{1/s} + b$ arise in a range of economic,
financial and control problems, where $A$ is a linear operator acting on a
space of real-valued functions (or vectors) and $s$ is a nonzero real value. In
these applications, attention is focused on positive solutions. We provide a
simple and complete characterization of existence and uniqueness of positive
solutions under conditions on $A$ and $b$ that imply positivity.
