Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions

Alberto Boscaggin, Francesca Colasuonno, Benedetta Noris

Published 2018-06-15Version 1

We analyze existence, multiplicity and oscillatory behavior of positive radial solutions to a class of quasilinear equations governed by the Lorentz-Minkowski mean curvature operator. The equation is set in a ball or an annulus of $\mathbb R^N$, is subject to homogeneous Neumann boundary conditions, and involves a nonlinear term on which we do not impose any growth condition at infinity. The main tool that we use is the shooting method for ODEs.