Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three positive solutions of a nonlinear Dirichlet problem with competing
  power nonlinearities   This paper studies a nonlinear Dirichlet problem for the $p$-Laplacian
operator with nonlinearity consisting of power components. The problem under
consideration can be though of as a perturbation of the
Ambrosetti-Brezis-Cerami problem with concave-convex nonlinearity. The combined
effect of power components in the perturbed nonlinearity allows to establish a
higher order multiplicity of positive solutions. We study properties of the
perturbed energy functional and prove the existence of three positive solutions
to the problem at hand.

8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ