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

Haitao Yang

doi:10.3934/cpaa.2005.4.197

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2005, Volume 4, Issue 1: 187-198. Doi: 10.3934/cpaa.2005.4.197

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

Haitao Yang^1,

1.
Department of Mathematics, Zhejiang University, Hangzhou 310027

Received: February 29, 2004

Revised: July 31, 2004

Published: February 2005

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Abstract

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 $\gamma \in (0, 1)$.

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Mathematics Subject Classification: Primary 35j05, 35j25. Secondary 35B40.

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