Existence, uniqueness and stability of positive solutions for a class of semilinear elliptic systems

Abstract

We consider the stability of positive solutions
to semilinear elliptic systems under a new general sublinear condition and its variants.
Using the stability result and bifurcation theory,
we prove the existence and uniqueness
of positive solution and obtain the precise global bifurcation
diagram of the system being a single monotone solution curve.