Infinitely many solution for prescribed curvature problem on $S^N$

Details Infinitely many solution for prescribed curvature problem on $S^N$ Infinitely many solution for prescribed curvature problem on $S^N$

2008-04-25

arxiv.org/abs/0804.4030v1

Journal of Functional Analysis 258(2010)

Mathematics

Analysis of PDEs

40 pages

Scientific paper

We consider the following prescribed scalar curvature problem on $ S^N$ (*)$$\left\{\begin{array}{l} - \Delta_{S^N} u + \frac{N(N-2)}{2} u = \tilde{K} u^{\frac{N+2}{N-2}} {on} S^N, u >0 \end{array}\right. $$ where $ \tilde{K}$ is positive and rotationally symmetric. We show that if $\tilde{K}$ has a local maximum point between the poles then equation (*) has {\bf infinitely many non-radial positive} solutions, whose energy can be made arbitrarily large.

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