LAUSR

In this paper we prove the existence of infinitely many radial solutions of \begin{document}$ \Delta u + K(r)f(u) = 0 $\end{document} on the exterior of the ball of radius \begin{document}$ R>0 $\end{document} , \begin{document}$ B_{R} $\end{document} , centered at the origin in \begin{document}$ {\mathbb R}^{N} $\end{document} with \begin{document}$ u = 0 $\end{document} on \begin{document}$ \partial B_{R} $\end{document} and \begin{document}$ \lim_{r \to \infty} u(r) = 0 $\end{document} where \begin{document}$ N>2 $\end{document} , \begin{document}$ f $\end{document} is odd with \begin{document}$ f on \begin{document}$ (0, \beta) $\end{document} , \begin{document}$ f>0 $\end{document} on \begin{document}$ (\beta, \infty), $\end{document} \begin{document}$ f $\end{document} superlinear for large \begin{document}$ u $\end{document} and \begin{document}$ 0 with \begin{document}$ 2 for large \begin{document}$ r $\end{document} .