Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-bump solutions of $-\Delta u=K(x)u^{\frac{n+2}{n-2}}$ on lattices
  in $R^n$   We consider critical exponent semi-linear elliptic equation with coefficient
K(x) periodic in its first k variables, with 2k smaller than n-2. Under some
natural conditions on K near a critical point, we prove the existence of
multi-bump solutions where the centers of bumps can be placed in some lattices
in Rk, including infinite lattices. We also show that for 2k greater than or
equal to n-2, no such solutions exist.

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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg