Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicity of solutions on a Nehari set in an invariant cone   For $1<p<2$ and $q$ large, we prove the existence of two positive,
nonconstant, radial and radially nondreacreasing solutions of the supercritical
equation \[-\Delta_p u+u^{p-1}=u^{q-1}\] under Neumann boundary conditions, in
the unit ball of $\mathbb R^N$. We use a variational approach in an invariant
cone. We distinguish the two solutions upon their energy: one is a ground state
inside a Nehari-type subset of the cone, the other is obtained via a mountain
pass argument inside the Nehari set. As a byproduct of our proofs, we detect
the limit profile of the low energy solution as $q\to\infty$ and show that the
constant solution 1 is a local minimum on the Nehari set.

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The categories of this paper are: cs
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg