Solutions with clustered bubbles and a boundary layer of an elliptic problem

Liping Wang; Chunyi Zhao

doi:10.3934/dcds.2014.34.2333

Article Contents

2014, Volume 34, Issue 5: 2333-2357. Doi: 10.3934/dcds.2014.34.2333

This issue Previous Article Dimension estimates for arbitrary subsets of limit sets of a Markov construction and related multifractal analysis Next Article Vortex structures for Klein-Gordon equation with Ginzburg-Landau nonlinearity

Solutions with clustered bubbles and a boundary layer of an elliptic problem

Liping Wang^1, and
Chunyi Zhao^2,

1.
Department of mathematics, East China Normal University, 500 Dong Chuan Road, Shanghai 200241
2.
Department of Mathematics, East China Normal University, Shanghai 200241

Received: May 31, 2013

Revised: July 31, 2013

Published: April 2014

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Abstract

We study positive solutions of the equation $ε^2 \Delta u - u + u^\frac{n+2}{n-2} = 0$ where $ε >0$ is small, with Neumann boundary condition in a unit ball $B\subset\mathbb R^3$. We prove the existence of solutions with multiple interior bubbles near the center and a boundary layer. The method may also be used to the case $n=4$, $5$ and get the analogous results.

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Mathematics Subject Classification: 35J25, 35J61.

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