## Topological Methods in Nonlinear Analysis

### Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball

#### Abstract

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation $$\begin{cases} \displaystyle -{\rm div}\bigg( \frac{\nabla v} {\sqrt{1 - |\nabla v|^2}}\bigg)= f(|x|,v) &\quad \text{in } B_R, \\ v=0 & \quad \text{on } \partial B_R, \end{cases}$$ where $B_R$ is a ball in $\mathbb{R}^N$ ($N\ge 2$). According to the behaviour of $f=f(r,s)$ near $s=0$, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 44, Number 1 (2014), 23-39.

Dates
First available in Project Euclid: 11 April 2016

https://projecteuclid.org/euclid.tmna/1460381468

Mathematical Reviews number (MathSciNet)
MR3289006

Zentralblatt MATH identifier
1366.35029

#### Citation

Coelho, Isabel; Corsato, Chiara; Rivetti, Sabrina. Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball. Topol. Methods Nonlinear Anal. 44 (2014), no. 1, 23--39. https://projecteuclid.org/euclid.tmna/1460381468

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