Year: 2011
Type: article
Abstract: We investigate the asymptotic behavior of positive solutions to the elliptic equation (0.1) ${\Delta}u+|x|^{l_1}u^p+|x|^{l_2}u^q=0$ in $\mathbb{R}^n$ . We obtain a conclusion that, for n $\geq$ 3, -2 < $l_2$ < $l_1$ $\leq$ 0 and q > p > 1, any positive radial solution to (0.1) has the following properties: $lim_{r{\rightarrow}{\infty}}r^{\frac{2+l_1}{p-1}}\;u$ and $lim_{r{\rightarrow}0}r^{\frac{2+l_2}{q-1}}\;u$ always exist if $\frac{n+1_1}{n-2}$ < p < q, $p\;{\neq}\;\frac{n+2+2l_1}{n-2}$ , $q\;{\neq}\;\frac{n+2+2l_2}{n-2}$ . In addition, we prove that the singular positive solution of (0.1) is unique under some conditions.
Authors: Baishun Lai, Qing Luo, Shuqing Zhou
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: 非线性发展方程及其定常解的一些研究, 偏微分方程中几个问题的研究
OpenAlex ID: W2093616631