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

TL;DR

This paper investigates the existence, multiplicity, and oscillatory nature of positive radial solutions to a class of quasilinear Minkowski-curvature equations with Neumann boundary conditions, using the shooting method for ODEs.

Contribution

It provides new results on positive solutions for Minkowski-curvature equations without growth restrictions on the nonlinear term.

Findings

Established conditions for existence of solutions.

Identified multiple solutions and oscillatory behaviors.

Applied shooting method to analyze boundary value problems.

Abstract

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.