Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pairs of nontrivial solutions to concave-linear-convex type elliptic
  problems   We obtain a pair of nontrivial solutions for a class of concave-linear-convex
type elliptic problems that are either critical or subcritical. The solutions
we find are neither local minimizers nor of mountain pass type in general. They
are higher critical points in the sense that they each have a higher critical
group that is nontrivial. This fact is crucial for showing that our solutions
are nontrivial. We also prove some intermediate results of independent interest
on the localization and homotopy invariance of critical groups of functionals
involving critical Sobolev exponents.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th