
Journal of Convex Analysis 22 (2015), No. 1, 061080 Copyright Heldermann Verlag 2015 Existence of Many Nonradial Positive Solutions of the Hénon Equation in R^{3} Naoki Shioji Dept. of Mathematics, Faculty of Engineering, Yokohama National University, Tokiwadai, Hodogayaku, Yokohama 2408501, Japan shioji@ynu.ac.jp [Abstractpdf] Let $B_1$ be the open unit ball in $\mathbf{R}^3$ and let $2 0$ such that for each $\alpha\geq \alpha_0$, there exist
at least $m$ nonradial positive solutions of
$$
\Delta u = x^\alpha u(x)^{p2}u(x)
\quad\text{in $B_1$,}\qquad
u = 0 \quad\text{on $\partial B_1$,}
$$
which are mutually nonequivalent if $m\geq 2$.
