Let
BR be the ball of radius
R in
RN with
N≥2. We consider the nonconstant radial positive solutions of elliptic systems of the form
where
f and
g are nondecreasing in each component. With few assumptions on the nonlinearities, we apply bifurcation theory to show the existence of at least one nonnegative, nonconstant and nondecreasing solution.