Minimal energy solutions and infinitely many bifurcating branches for a class of saturated nonlinear Schrödinger systems

2015/03/31 by Mandel, Rainer
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.08974

Abstract

We prove a conjecture which was recently formulated by Maia, Montefusco, Pellacci saying that minimal energy solutions of the saturated nonlinear Schrödinger system - Δu + λ₁ u amp;= (αu(αu²+βv²))/(1+s(αu²+βv²)) \qquadin ℝⁿ, \newline - Δv + λ₂ v amp;= (βv(αu²+βv²))/(1+s(αu²+βv²))\qquadin ℝⁿ are necessarily semitrivial whenever α,β,λ₁,λ₂>0 and 0

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