Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and local uniqueness of bubbling solutions for poly-harmonic
  equations with critical growth   \begin{abstract} We consider the following poly-harmonic equations with
critical exponents: \begin{equation}\label{P} (-\Delta)^m u
=K(y)u^{\frac{N+2m}{N-2m}},\;\;\; u>0\;\;\;\hbox{in} \mathbb{R}^N,
\end{equation} where $N> 2m+2,m\in\mathbb{N}_{+}, K(y)$ is positive and
periodic in its first $k$ variables $(y_1,\cdots, y_k)$, $1\leq
k<\frac{N-2m}{2}$. Under some conditions on $K(y)$ near its critical point, we
prove not only that problem~\eqref{P} admits solutions with infinitely many
bubbles, but also that the bubbling solutions obtained in our existence result
are locally unique. This local uniqueness result implies that some bubbling
solutions preserve the symmetry of the scalar curvature $K(y).$

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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: physics