American Institute of Mathematical Sciences

March  2005, 4(1): 187-198. doi: 10.3934/cpaa.2005.4.197

On the existence and asymptotic behavior of large solutions for a semilinear elliptic problem in $R^n$

 1 Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received  March 2004 Revised  August 2004 Published  December 2004

In this paper, we give an existence result for nonradial large solutions of the semilinear elliptic equation $\Delta u =p(x)f(u)$ in $R^N (N\ge 3)$, where $f$ is assumed to satisfy $(f_1)$ and $(f_2)$ below. The asymptotic behavior of the large solutions at infinity are also studied in the sublinear case that $f(u)$ behaves like $u^{\gamma}$ at $\infty$ for $\gamma \in (0, 1)$.
Citation: Haitao Yang. On the existence and asymptotic behavior of large solutions for a semilinear elliptic problem in $R^n$. Communications on Pure & Applied Analysis, 2005, 4 (1) : 187-198. doi: 10.3934/cpaa.2005.4.197
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