Classification of positive solutions of semilinear elliptic equations with Hardy term Abstract References Full Text (393.7K)
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.
Received: September 2012; Revised: July 2013; Published: November 2013. |