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

• 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 $\gamma \in (0, 1)$.
Mathematics Subject Classification: Primary 35j05, 35j25. Secondary 35B40.

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