Uniqueness results for semilinear elliptic systems on \Rⁿ

2013/05/27 by Mandel, R.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1305.6157

Abstract

In this paper we establish uniqueness criteria for positive radially symmetric finite energy solutions of semilinear elliptic systems of the form \beginaligned - Δu amp;= f(|x|,u,v)\quadin\Rⁿ, - Δv amp;= f(|x|,v,u)\quadin\Rⁿ. \endaligned As an application we consider the following nonlinear Schrödinger system \beginaligned - Δu + u amp;= u^2q-1 + b u^q-1v^q\quadin\Rⁿ, - Δv + v amp;= v^2q-1 + b v^q-1u^q \quadin\Rⁿ. \endaligned for b>0 and exponents q which satisfy 1

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