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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