Asymptotic behavior of positive solutions of semilinear elliptic equations in $R^{n}$

Details Asymptotic behavior of positive solutions of semilinear elliptic equations in $R^{n}$ Asymptotic behavior of positive solutions of semilinear elliptic equations in $R^{n}$

2010-01-15

arxiv.org/abs/1001.2587v1

Mathematics

Analysis of PDEs

17

Scientific paper

We will investigate the asymptotic behavior of positive solutions of the elliptic equation \Delta u+|x|^{l_{1}}u^{p}+|x|^{l_{2}}u^{q}=0 {in} R^{n}. We establish that for $n\geq 3$ and $q>p>1$, any positive radial solution of (0.1) has the following property: $\lim_{r\to\infty}r^{\frac{2+l_{1}}{p-1}}u$ and $\lim_{r\to0}r^{\frac{2+l_{2}}{q-1}}u$ always exist if $\frac{n+l_{1}}{n-2}

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