Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The logistic elliptic equation with the nonlinear boundary condition
  arising from coast fishery harvesting   Let $0<q<1<p$. In this study, we investigate positive solutions of the
logistic elliptic equation $-\Delta u = u(1-u^{p-1})$ in a smooth bounded
domain $\Omega$ of $\mathbb{R}^N$, $N\geq1$, with the nonlinear boundary
condition $\frac{\partial u}{\partial \nu}=-\lambda u^q$ on $\partial\Omega$.
This nonlinear boundary condition arises from coast fishery harvesting. When
$p>1$ is subcritical, we prove that in the case of $\lambda_{\Omega}>1$, there
exist at least two positive solutions for $\lambda>0$ sufficiently small but no
positive solutions for $\lambda>0$ large enough. In the case of
$\lambda_{\Omega}<1$, there exists at least one positive solution for every
$\lambda>0$. Here, $\lambda_{\Omega}>0$ is the smallest eigenvalue of $-\Delta$
under the Dirichlet boundary condition. An interpretation of our main results
from an ecological viewpoint is presented.

25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat