We discuss existence and multiplicity of bounded variation solutions of the mixed problem for the prescribed mean curvature equation$$-{\rm div } \Big({\nabla u}/{ \sqrt{1+{|\nabla u|}^2}}\Big) = f(x,u) \hbox{\, in \Omega},\quadu=0 \hbox{\, on \Gamma_{D}}, \quad \partial u / \partial \nu =0 \hbox{\, on  \Gamma_{N}},$$where $\Gamma_{D}$ is an open subset of $\partial \Omega$ and $\Gamma_{N}=\partial \Omega\setminus \Gamma_{D}$. Our approach is based on variational techniques and a lower and upper solutions method specially developed for this problem.

### Existence and multiplicity results for the prescribed mean curvature equation via lower and upper solutions

#### Abstract

We discuss existence and multiplicity of bounded variation solutions of the mixed problem for the prescribed mean curvature equation$$-{\rm div } \Big({\nabla u}/{ \sqrt{1+{|\nabla u|}^2}}\Big) = f(x,u) \hbox{\, in \Omega},\quadu=0 \hbox{\, on \Gamma_{D}}, \quad \partial u / \partial \nu =0 \hbox{\, on  \Gamma_{N}},$$where $\Gamma_{D}$ is an open subset of $\partial \Omega$ and $\Gamma_{N}=\partial \Omega\setminus \Gamma_{D}$. Our approach is based on variational techniques and a lower and upper solutions method specially developed for this problem.
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2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2280921
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