Pairs of positive radial solutions for a Minkowski-curvature Neumann problem with indefinite weight

Abstract

We prove the existence of a pair of positive radial solutions for the Neumann boundary value problem div(∇u1−|∇u|2)+λa(|x|)up=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 ∫Ba(|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.