- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:05
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2005
4
Arbitrary Number of Positive Solutions For an Elliptic Problem with Critical Nonlinearity
Olivier
Rey
École Polytechnique, PALAISEAU CEDEX, FRANCE
Juncheng
Wei
University of British Columbia, VANCOUVER, CANADA
semilinear elliptic Neumann problems, critical Sobolev exponent, blow-up
We show that the critical nonlinear elliptic Neumann problem \[ \Delta u -\mu u + u^{7/3} = 0 \ \ \mbox{in} \ \Om, \ \ u >0 \ \mbox{in} \ \Om \ \mbox{and} \ \frac{ \partial u}{\partial \nu} = 0 \ \ \mbox{on} \ \partial \Om\] where $\Om$ is a bounded and smooth domain in $\R^5$, has arbitrarily many solutions, provided that $\mu>0$ is small enough. More precisely, for any positive integer $K$, there exists $\mu_K >0$ such that for $0
Partial differential equations
General
449
476
10.4171/JEMS/35
http://www.ems-ph.org/doi/10.4171/JEMS/35