We prove the existence of multiple positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space \begin{equation*} \begin{cases} -{\rm div}\Big( \nabla u /\sqrt{1 - |\nabla u|^2}\Big)= f(x,u, \nabla u) & \hbox{ in } \Omega, \\ u=0& \hbox{ on } \partial \Omega. \end{cases} \end{equation*} Here $\Omega$ is a bounded regular domain in $\RR^N$ and the function $f=f(x,s,\xi)$ is either sublinear, or superlinear, or sub-superlinear near $s=0$. The proof combines topological and variational methods.

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

CORSATO, CHIARA;OBERSNEL, Franco;OMARI, PIERPAOLO;RIVETTI, SABRINA
2013

Abstract

We prove the existence of multiple positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space \begin{equation*} \begin{cases} -{\rm div}\Big( \nabla u /\sqrt{1 - |\nabla u|^2}\Big)= f(x,u, \nabla u) & \hbox{ in } \Omega, \\ u=0& \hbox{ on } \partial \Omega. \end{cases} \end{equation*} Here $\Omega$ is a bounded regular domain in $\RR^N$ and the function $f=f(x,s,\xi)$ is either sublinear, or superlinear, or sub-superlinear near $s=0$. The proof combines topological and variational methods.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2589620
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