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September/October 2009 Existence and multiplicity results for the prescribed mean curvature equation via lower and upper solutions
Franco Obersnel, Pierpaolo Omari
Differential Integral Equations 22(9/10): 853-880 (September/October 2009).

Abstract

We discuss existence and multiplicity of bounded variation solutions of the mixed problem for the prescribed mean curvature equation \begin{equation*} -{\rm div } \Big({\nabla u}/{ \sqrt{1+{|\nabla u|}^2}}\Big) = f(x,u) \hbox{\, in $\Omega$}, \quad u=0 \hbox{\, on $\Gamma_{D}$}, \quad \partial u / \partial \nu =0 \hbox{\, on $ \Gamma_{N}$}, \end{equation*} 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.

Citation

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Franco Obersnel. Pierpaolo Omari. "Existence and multiplicity results for the prescribed mean curvature equation via lower and upper solutions." Differential Integral Equations 22 (9/10) 853 - 880, September/October 2009.

Information

Published: September/October 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35131
MathSciNet: MR2553060

Subjects:
Primary: 35J93
Secondary: 35J20

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.22 • No. 9/10 • September/October 2009
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