Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely many solution for prescribed curvature problem on $S^N$   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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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin