Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive steady states of an indefinite equation with a nonlinear
  boundary condition: existence, multiplicity, stability and asymptotic
  profiles   We investigate positive steady states of an indefinite superlinear
reaction-diffusion equation arising from population dynamics, coupled with a
nonlinear boundary condition. Both the equation and the boundary condition
depend upon a positive parameter $\lambda$, which is inversely proportional to
the diffusion rate. We establish several multiplicity results when the
diffusion rate is large and analyze the asymptotic profiles and the stability
properties of these steady states as the diffusion rate grows to infinity. In
particular, our results show that in some cases bifurcation from zero and from
infinity occur at $\lambda=0$. Our approach combines variational and
bifurcation techniques.

29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org