Positive ground states for a system of Schrödinger equations with critically growing nonlinearities

2014/03/13 by d'Avenia, Pietro, Mederski, Jarosław
#35A01 #35B33 #35J50 #35J57 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1403.3211

Abstract

We study the following problem \begincases -Δu = λu + u^{2^*-2} v amp; \hboxin Ω,
-Δv= μv^{2^*-1} + u^{2^*-1} amp; \hboxin Ω,
ugt; 0,vgt; 0 amp; \hboxin Ω,
u=v=0 amp; \hboxon ∂ Ω, \endcases where Ω is a bounded domain of ℝ^N, N≥ 4, 2^*=2N/(N-2), λ∈ℝ and μ≥ 0 and we obtain existence and nonexistence results, depending on the value of the parameters λ and μ.

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