On Helmholtz equation and Dancer's type entire solutions for nonlinear elliptic equations

2016/04/08 by Yong Liu, Juncheng Wei, Liu, Yong +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1604.02231

11 pages

arxiv created 2016/04/08 · arxiv updated 2016/04/11

Abstract

Starting from a bound state (positive or sign-changing) solution to -Δω_m =|ω_m|^p-1 ω_m -ω_m in \Rⁿ, ω_m ∈ H² (\Rⁿ) and solutions to the Helmholtz equation Δu₀ + λu₀=0 in \Rⁿ, λ>0, we build new Dancer's type entire solutions to the nonlinear scalar equation -Δu =|u|^p-1 u-u in \R^m+n.

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