Abstract

Let B1B_1 be the open unit ball in R3\mathbb{R}^3 and let 2<p<62<p<6. We show that for each m∈Nm\in \mathbb{N}, there exists α0>0\alpha_0>0 such that for each α≥α0\alpha\geq \alpha_0, there exist at least mm nonradial positive solutions of −Δu=∣x∣α∣u(x)∣p−2u(x)in B1,u=0on ∂B1,-\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≥2m\geq 2.

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Naoki Shioji

Dept. of Mathematics, Faculty of Engineering, Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan

shioji@ynu.ac.jp

Keywords

  • Hénon equation
  • multiplicity of positive solutions
  • concentration compactness principle
  • Poincaré's inequalities

Mathematics Subject Classification

35J20, 35J61

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Suggested citation

N. Shioji. “Existence of Many Nonradial Positive Solutions of the Hénon Equation in R^3.” Journal of Convex Analysis 22 (2015), No. 1, 61–80. https://doi.org/10.68381/jca22004

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