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Asymptotic behaviour of positive solutions of semilinear elliptic problems with increasing powers
Published online by Cambridge University Press: 28 September 2021
Abstract
We prove existence results of two solutions of the problem
\[ \begin{cases} L(u)+u^{m-1}=\lambda u^{p-1} & \text{in}\ \Omega,\\ u>0 & \text{in}\ \Omega,\\ u=0 & \text{on}\ \partial \Omega, \end{cases} \]
$L(v)=-\textrm {div}(M(x)\nabla v)$ is a linear operator,
$p\in (2,2^{*}]$ and
$\lambda$ and
$m$ sufficiently large. Then their asymptotical limit as
$m\to +\infty$ is investigated showing different behaviours.
Keywords
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 5 , October 2022 , pp. 1233 - 1250
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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