Bulletin of the Australian Mathematical Society Bull. Austral. Math. Soc. 0004-9727 ALNBAB 2005 72 3 10.wxyz/CV72P3 http://www.austms.org.au/Publ/Bulletin/V72P3/ Tsing-San Hsu Huei-Li Lin 13 February 2006 2006 2 13 349 370 723-5127-HsuLin-2005 10.wxyz/C2005V72P3p349 http://www.austms.org.au/Publ/Bulletin/V72P3/723-5127-HsuLin/ 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 ${\mathbb {R}^N}$. 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