Multiple positive solutions for Dirichlet problem of prescribed mean curvature equations in Minkowski spaces
In this article, we consider the Dirichlet problem for the prescribed mean curvature equation in the Minkowski space, $$\displaylines{ -\hbox{div}\Big(\frac {\nabla u}{\sqrt{1-|\nabla u|^2}}\Big) =\lambda f(u) \quad \text{in } B_R,\cr u=0 \quad \text{on } \partial B_R, }$$ where $B_R:=\{x\in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/180/abstr.html |
| Summary: | In this article, we consider the Dirichlet problem for the prescribed
mean curvature equation in the Minkowski space,
$$\displaylines{
-\hbox{div}\Big(\frac {\nabla u}{\sqrt{1-|\nabla u|^2}}\Big)
=\lambda f(u) \quad \text{in } B_R,\cr
u=0 \quad \text{on } \partial B_R,
}$$
where $B_R:=\{x\in \mathbb{R}^N: |x|< R\}$, $\lambda>0$
is a parameter and $f:[0, \infty)\to\mathbb{R}$ is continuous. We apply
some standard variational techniques to show how changes in the sign of
f lead to multiple positive solutions of the above problem for
sufficiently large $\lambda$. |
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| ISSN: | 1072-6691 |