Degenerate riccati equations with unbounded coefficients arising in transport theory

Of concern is the degenerate Riccati equation of the form TR+RT=TA+TBR+RTC+RTDR (?). This models a certain transport equation in the half-space. Our first result will concern a unique, positive solution of the operator equation SR+RT=K in a anach space equipped with a cone structure. We then proceed to prove existence of positive solutions for (?) on an L¹ space of σ-finite measure and a Banach space X, respectively, under different assumptions. Some estimates of the solution with respect to certain norms are obtained.