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Nonlinear parabolic equations with a lower order term and $L^1$ data
Some properties of positive radial solutions for some semilinear elliptic equations
| 1. | College of Mathematics and Econometrics, Hunan University, Changsha 410082, China |
$ \Delta h = \frac{1}{\alpha } h^{ -\alpha }-p(r)$ in $R^N( N\geq3 ),$
where $ \alpha >1$ and the monotone decreasing function $p(r)$ satisfying $\lim_{r\rightarrow \infty}p(r)=c>0.$ In this paper we show that for any $ \eta >0 $ there is a unique radial solution $ h(r) $ with $ h(0)=\eta $ and $ h(r)$ is oscillatory in $ [0, \infty )$. We prove $ \lim_{r \rightarrow \infty } h(r)=( \alpha c)^{-\frac{1}{\alpha}}. $ We also obtain similar properties of singular solutions, of which the zero set is nonempty.
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