Pairs of positive radial solutions for a Minkowski-curvature Neumann problem with indefinite weight. (July 2020) - Boscaggin, Alberto; Feltrin, Guglielmo
Abstract: We prove the existence of a pair of positive radial solutions for the Neumann boundary value problem div ( ∇ u 1 − | ∇ u | 2 ) + λ a ( | x | ) u p = 0, in B, ∂ ν u = 0, on ∂ B, where B is a ball centered at the origin, a ( | x | ) is a radial sign-changing function with ∫ B a ( | x | ) d x < 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.