Multiplicity of solutions for the Minkowski-curvature equation via shooting method

TL;DR

This paper establishes the existence and multiple solutions of a nonlinear Minkowski-curvature problem in a ball with Neumann boundary conditions using the shooting method for ODEs.

Contribution

It introduces a novel application of the shooting method to prove multiplicity of solutions for the Minkowski-curvature equation in Lorentz-Minkowski space.

Findings

Proved existence of multiple radial solutions

Demonstrated oscillatory behavior of solutions

Applied shooting method effectively to nonlinear PDEs

Abstract

In this paper we prove the existence and the multiplicity of radial positive oscillatory solutions for a nonlinear problem governed by the mean curvature operator in the Lorentz-Minkowski space. The problem is set in a ball $B_R$ of $\mathbb R^N$ and is subject to Neumann boundary conditions. The main tool used is the shooting method for ODEs.