| Title:
|
A population biological model with a singular nonlinearity (English) |
| Author:
|
Rasouli, Sayyed Hashem |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
257-264 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the existence of positive solutions of the singular nonlinear semipositone problem of the form $$ \begin {cases} -{\rm div}(|x|^{-\alpha p}|\nabla u|^{p-2}\nabla u)=|x|^{-(\alpha +1)p+\beta } \Big (a u^{p-1}-f(u)-\dfrac {c}{u^{\gamma }}\Big ), \quad x\in \Omega ,\\ u=0, \quad x\in \partial \Omega , \end {cases} $$ where $\Omega $ is a bounded smooth domain of ${\mathbb R}^N$ with $0\in \Omega $, $1<p<N$, $0\leq \alpha < {(N-p)}/{p}$, $\gamma \in (0,1)$, and $a$, $\beta $, $c$ and $\lambda $ are positive parameters. Here $f\colon [0,\infty )\to {\mathbb R}$ is a continuous function. This model arises in the studies of population biology of one species with $u$ representing the concentration of the species. We discuss the existence of a positive solution when $f$ satisfies certain additional conditions. We use the method of sub-supersolutions to establish our results. (English) |
| Keyword:
|
population biology |
| Keyword:
|
infinite semipositone |
| Keyword:
|
sub-supersolution |
| MSC:
|
35A01 |
| MSC:
|
35B09 |
| MSC:
|
35J60 |
| MSC:
|
35J62 |
| MSC:
|
35J65 |
| MSC:
|
35J75 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 06362225 |
| idMR:
|
MR3232629 |
| DOI:
|
10.1007/s10492-014-0053-7 |
| . |
| Date available:
|
2014-05-20T07:31:08Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143771 |
| . |
| Reference:
|
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