Radial positive solutions of nonlinear elliptic systems with Neumann boundary conditions

We consider radial positive solutions of elliptic systems of the form{−Δu+u=α(|x|)f(u,v)inBR,−Δv+v=β(|x|)g(u,v)inBR,∂νu=∂νv=0on∂BR, where essentially α, β are assumed to be radially nondecreasing weights and f, g are nondecreasing in each component. We show the existence of at least one nondecreasing nontrivial radial solutions. Our result is sharp and is a complement for one of the main results in Bonheure et al. (2013) [2]. The proof of our main result is based upon bifurcation techniques.