Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions

Let B-R be the ball of radius R in R-N with N >= 2. We consider the nonconstant radial positive solutions of elliptic systems of the form -Delta u + u = f(u, v) in B-R, -Delta v +v = g(u, v) in B-R, partial derivative(nu)u =partial derivative(nu)v = 0 on partial derivative B-R, 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. (C) 2016 Elsevier Inc. All rights reserved.