# American Institute of Mathematical Sciences

January  2008, 21(1): 333-351. doi: 10.3934/dcds.2008.21.333

## Solutions with interior bubble and boundary layer for an elliptic problem

 1 Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong, China 2 Department of Mathematics, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

Received  January 2007 Revised  August 2007 Published  February 2008

We study positive solutions of the equation $\varepsilon^2\Delta u - u + u^{\frac{n+2}{n-2}} = 0$, where $n=3,4,5$, and $\varepsilon > 0$ is small, with Neumann boundary condition in a smooth bounded domain $\Omega \subset R^n$. We prove that, along some sequence $\{\varepsilon_j \}$ with $\varepsilon_j \to 0$, there exists a solution with an interior bubble at an innermost part of the domain and a boundary layer on the boundary $\partial\Omega$.
Citation: Liping Wang, Juncheng Wei. Solutions with interior bubble and boundary layer for an elliptic problem. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 333-351. doi: 10.3934/dcds.2008.21.333
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