Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and non-existence results for a logistic-type equation on
  manifolds   We study the steady state solutions of a generalized logistic type equation
on a complete Riemannian manifold. We provide sufficient conditions for
existence, respectively non-existence of positive solutions, which depend on
the relative size of the coefficients and their mutual interaction with the
geometry of the manifold, which is mostly taken into account by means of
conditions on the volume growth of geodesic balls.

5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org