Solutions with interior bubble and boundary layer for an elliptic Neumann problem with critical nonlinearity

We study positive solutions of the equation ${\mathrm{?}}^2\mathrm{\Delta }u?u+u^{\frac{n+2}{n?2}}=0$, where $n=3,4,5$ and $\mathrm{?}>0$ is small, with Neumann boundary condition in a unit ball B. We prove the existence of solutions with an interior bubble at the center and a boundary layer at the boundary ?B. To cite this article: J. Wei, S. Yan, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Three examples of three-dimensional continued fractions in the sense of Klein

The problem of the investigation of the simplest n-dimensional continued fraction in the sense of Klein for $n?2$ was posed by V. Arnold. The answer for the case $n=2$ can be found in the works of E. Korkina (1995) and G. Lachaud (1995). In present Note we study the case $n=3$. To cite this article: O. Karpenkov, C. R. Acad. Sci. Paris, Ser. I 343 (2006).