On multiple positive ground state solutions for a mean curvature equation in Minkowski space

TL;DR

This paper investigates how sign changes in the nonlinearity of a mean curvature equation in Minkowski space lead to multiple radial ground state solutions for large parameter values.

Contribution

It demonstrates the existence of multiple solutions caused by nonlinearity sign changes in a mean curvature equation in Minkowski space.

Findings

Multiple radial ground state solutions exist for large mbda.

Sign changes in nonlinearity induce solution multiplicity.

Results apply to equations in rminkowski space with N or higher.

Abstract

In this paper, we show how changes in the sign of nonlinearity leads to multiple radial ground state solutions of the mean curvature equation $ \nabla\cdot \Big[\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\Big] +\lambda f(u)=0\ \ \text{in} \ \mathbb{R}^N $ for sufficiently large $\lambda$ with $N\geq 2$.