  In a previous paper(2021), the author studied the asymptotic behavior of
coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both
cross-diffusion coefficients tend to infinity at the same rate. As a result, he
proved that the asymptotic behavior can be characterized by a limiting system
that consists of a semilinear elliptic equation and an integral constraint.
This paper studies the set of solutions of the limiting system. The first main
result gives sufficient conditions for the existence/nonexistence of
nonconstant solutions to the limiting system by a topological approach using
the Leray-Schauder degree. The second main result exhibits a bifurcation
diagram of nonconstant solutions to the one-dimensional limiting system by
analysis of a weighted time-map and a nonlocal constraint.
