On isolated singular solutions of semilinear Helmholtz equation
On isolated singular solutions of semilinear Helmholtz equation
Our purpose of this paper is to study isolated singular solutions of semilinear Helmholtz equation \begin{document}$ -\Delta u-u = Q|u|^{p-1}u \quad{\rm in}\ \ \mathbb{R}^N\setminus\{0\},\ \qquad\lim\limits_{|x|\to0}u(x) = +\infty, $\end{document} where \begin{document}$ N\geq 2 $\end{document}, \begin{document}$ p>1 $\end{document} and the potential \begin{document}$ Q: \mathbb{R}^N\to (0,+\infty) $\end{document} is a Hölder continuous function satisfying …