Nonradial solutions for the Hénon equation close to the threshold

2017/08/30 by Figueroa, Pablo, Neves, Sérgio L. N.
#35B32 #35J25 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.09112

Abstract

We consider the Hénon problem \ - - Δu = |x|^α u^{(N+2+2α)/(N-2)-ε} · amp; in B₁,
u · gt; 0 · amp; in B₁,
u=0 · amp; on ∂ B₁, . where B₁ is the unit ball in \mathbb R^N and N\geqslant 3. For ε > 0 small enough, we use α as a paramenter and prove the existence of a branch of nonradial solutions that bifurcates from the radial one when α is close to an even positive integer.

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