Chiara Corsato

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

Abstract We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation . Depending on the behaviour of f = f (t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

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

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation

The Dirichlet problem for gradient dependent prescribed mean curvature equations in the Lorentz–Minkowski space

\cases \displaystyle -\text{\rm div}\bigg( \frac{\nabla v} {\sqrt{1 - |\nabla v|^2}}\bigg)= f(|x|,v) &\quad \text{in } B_R, \\ \displaystyle v=0 & \quad \text{on } \partial B_R, \endcases

Generalising the Pari-Mutuel Model

where

Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space

B_R

On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space

is a ball in

The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions

\mathbb{R}^N

Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape

(