Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 22 (2015), No. 1, 061--080Copyright Heldermann Verlag 2015 Existence of Many Nonradial Positive Solutions of the Hénon Equation in R3 Naoki Shioji Dept. of Mathematics, Faculty of Engineering, Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan shioji@ynu.ac.jp [Abstract-pdf] Let $B_1$ be the open unit ball in $\mathbf{R}^3$ and let $20$ such that for each $\alpha\geq \alpha_0$, there exist at least $m$ nonradial positive solutions of $$-\Delta u = |x|^\alpha |u(x)|^{p-2}u(x) \quad\text{in B_1,}\qquad u = 0 \quad\text{on \partial B_1,}$$ which are mutually nonequivalent if $m\geq 2$. Keywords: Henon equation, multiplicity of positive solutions, concentration compactness principle, Poincare's inequalities. MSC: 35J20, 35J61 [ Fulltext-pdf  (190  KB)] for subscribers only.