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Journal of the London Mathematical Society 2006 74(2):415-440; doi:10.1112/S0024610706023027
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© The London Mathematical Society 2006

BOUNDARY CONCENTRATION IN RADIAL SOLUTIONS TO A SYSTEM OF SEMILINEAR ELLIPTIC EQUATIONS

Teresa D'Aprile and Juncheng Wei

Dipartimento di Matematica via E. Orabona 4, 70125 Bari, Italy daprile{at}dm.uniba.it
Department of Mathematics, The Chinese University of Hong Kong Shatin, Hong Kong wei{at}math.cuhk.edu.hk

Received 4 March 2005. Revision received 9 November 2005.

We study concentration phenomena for the system

Formula
in the unit ball B1 of R3 with Dirichlet boundary conditions. Here {varepsilon}, {delta}, {gamma} > 0 and p > 1. We prove the existence of positive radial solutions ({upsilon}{varepsilon}, {varphi}{varepsilon}) such that {upsilon}{varepsilon} concentrates at a distance ({varepsilon}/2)|log {varepsilon}| away from the boundary {partial} B1 as the parameter {varepsilon} tends to 0. The approach is based on a combination of Lyapunov–Schmidt reduction procedure together with a variational method.


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