@article {HsuLin2005,
 author="Tsing-San Hsu and Huei-Li Lin",
 title={Bifurcation of positive entire solutions for a semilinear elliptic equation},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="3",
 pages="349--370",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="25th April, 2005",
 classmath="35J20, 35J60",
 publisher={AMPAI, Australian Mathematical Society},
 url="http://www.austms.org.au/Publ/Bulletin/V72P3/723-5127-HsuLin/index.shtml",
 acknowledgement={},
 abstract={ In this paper, we consider the nonhomogeneous semilinear elliptic equation $$-\Delta u+u=\lambda K(x)u^p+h(x)\mbox { in }{\mathbb {R}^N}, u>0\mbox { in }{\mathbb {R}^N}\mbox { }, u\in H^1({\mathbb {R}^N} ), \leqno {(*)_\lambda } $$where $\lambda \geq 0$, $1<p<({N+2})/({N-2})$, if $N\ge 3$, $1<p<\infty $, if $N=2$, $h(x)\allowbreak \in H^{-1}({\mathbb {R}^N})$, $0\not \equiv h(x)\geq 0$ in ${\mathbb {R}^N}$, $K(x)$ is a positive, bounded and continuous function on ${\mathbb {R}^N}$. We prove that if $K(x)\geq K_\infty >0$ in ${\mathbb {R}^N}$, and $\lim \limits _{|x|\rightarrow \infty }K(x)=K_{\infty }$, then there exists a positive constant $\lambda ^*$ such that $(*)_\lambda $ has at least two solutions if $\lambda \in (0,\lambda ^*)$ and no solution if $\lambda >\lambda ^*$. Furthermore, $(*)_\lambda $ has a unique solution for $\lambda =\lambda ^*$ provided that $h(x)$ satisfies some suitable conditions. We also obtain some further properties and bifurcation results of the solutions of $(*)_\lambda $ at $\lambda =\lambda ^*$. }
}