Classification of positive solutions of semilinear elliptic equations with Hardy term

Pages: 31 - 39, Issue special, November 2013

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Soohyun Bae - Hanbat National University, Daejeon 305-719, South Korea (email)

Abstract: We study the elliptic equation $\Delta u+\mu/|x|^2+K(|x|)u^p=0$ in $\mathbb{R}^n \setminus \left \{ 0 \right \}$, where $n\geq1$ and $p>1$. In particular, when $K(|x|)=|x|^l$, a classification of radially symmetric solutions is presented in terms of $\mu$ and $l$. Moreover, we explain the separation structure for the equation, and study the stability of positive radial solutions as steady states.

Keywords:  Semilinear elliptic equation, positive solution, singular solution, separation, stability.
Mathematics Subject Classification:  Primary: 35J61, 35B09, 35B40; Secondary: 35B35.

Received: September 2012;      Revised: July 2013;      Published: November 2013.