  We study in an unified fashion several quadratic vector and matrix equations
with nonnegativity hypotheses. Specific cases of such problems (QBD equations,
nonsymmetric algebraic Riccati equations, Lu's simple equation, Markovian
binary trees equations) have been studied extensively in the past by several
authors. Many of the results appearing here have already been proved for one or
more of the single instances of the problems, resorting to specific
characteristics of the problem. In some cases the proofs we present here are
mere rewriting of the original proofs with a little change of notation to adapt
them to our framework, but in some cases we are effectively able to remove some
hypotheses and generalize the results by abstracting the specific aspects of
each problem.
