Electronic Journal of Differential Equations (2016-07-01)

Multiple positive solutions for Dirichlet problem of prescribed mean curvature equations in Minkowski spaces

  • Ruyun Ma,
  • Tianlan Chen

Journal volume & issue
Vol. 2016, no. 180,
pp. 1 – 7

Abstract

Read online

In this article, we consider the Dirichlet problem for the prescribed mean curvature equation in the Minkowski space, $$\displaylines{ -\hbox{div}\Big(\frac {\nabla u}{\sqrt{1-|\nabla u|^2}}\Big) =\lambda f(u) \quad \text{in } B_R,\cr u=0 \quad \text{on } \partial B_R, }$$ where $B_R:=\{x\in \mathbb{R}^N: |x|0$ is a parameter and $f:[0, \infty)\to\mathbb{R}$ is continuous. We apply some standard variational techniques to show how changes in the sign of f lead to multiple positive solutions of the above problem for sufficiently large $\lambda$.

Keywords