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High-energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponents*

Published online by Cambridge University Press:  14 November 2011

Zhi-Qiang Wang
Zhi-Qiang Wang
Affiliation:
Department of Mathematics, Utah State University, Logan, UT 84322, U.S.A
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Extract

We establish the existence of positive solutions with two peaks being located on the boundary of the domain for the problem −Δu + λu = up in antipodal invariant domains including ball domains with Neumann boundary conditions. Here p is the critical Sobolev exponent (N + 2)/(N − 2). The shape of the solutions and the location of the peaks are also studied.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 5 , 1995 , pp. 1003 - 1029
Copyright
Copyright © Royal Society of Edinburgh 1995

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