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.
Titolo: | Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space |
Autori: | |
Data di pubblicazione: | 2013 |
Rivista: | |
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. |
Handle: | http://hdl.handle.net/11368/2589620 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jmaa.2013.04.003 |
Appare nelle tipologie: | 1.1 Articolo in Rivista |
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