Article contents
Infinitely Many Solutions for the Prescribed Boundary Mean Curvature Problem in 𝔹N
Published online by Cambridge University Press: 20 November 2018
Abstract
We consider the prescribed boundary mean curvature problem in ${{\mathbb{B}}^{N}}$ with the Euclidean metric
where $\tilde{K}\left( x \right)$ is positive and rotationally symmetric on ${{\mathbb{S}}^{N-1}},{{2}^{\#}}=\frac{2\left( N-1 \right)}{N-2}$. We show that if $\tilde{K}\left( x \right)$ has a local maximum point, then this problem has infinitely many positive solutions that are not rotationally symmetric on ${{\mathbb{S}}^{N-1}}$.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2013
References
- 7
- Cited by