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This paper is contributed to the elliptic equation

(0.1) Δu+K(|x|)up+μf(|x|)=0,

where p>1, xRn, n⩾3, and μ⩾0 is a constant. We study the structure of positive radial solutions of (0.1) and obtain the uniqueness of solution decaying faster than rm at ∞ if μ is small enough under some assumptions on K and f, where m is the slow decay rate.


NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Differential Equations. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Differential Equations, 246, 2, (January 15, 2009) DOI# 10.1016/j.jde.2008.09.008.