We prove the existence of a pair of positive radial solutions for the Neumann boundary value problem div(∇u/sqrt(1-|∇u|^2))+λa(|x|)u^p=0, in B, ∂νu=0, on ∂B, where B is a ball centered at the origin, a(|x|) is a radial sign-changing function with ∫_B a(|x|)dx<0, p>1 and λ>0 is a large parameter. The proof is based on the Leray–Schauder degree theory and extends to a larger class of nonlinearities.
