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Journal of Convex Analysis 22 (2015), No. 1, 061--080
Copyright 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


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

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