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In this paper, we first obtain the existence of positive ground state solutions for the following critical fractional Laplacian system: (−Δ)su=μ1|u|2s∗−2u+αγ2s∗|u|α−2u|v|βinℝn,(−Δ)sv=μ2|v|2s∗−2v+βγ2s∗|u|α|v|β−2vinℝn, then we give a complete classification of positive ground… Click to show full abstract
In this paper, we first obtain the existence of positive ground state solutions for the following critical fractional Laplacian system: (−Δ)su=μ1|u|2s∗−2u+αγ2s∗|u|α−2u|v|βinℝn,(−Δ)sv=μ2|v|2s∗−2v+βγ2s∗|u|α|v|β−2vinℝn, then we give a complete classification of positive ground state solutions with different Morse index. More precisely, we show that if (u, v) be any positive ground state solution of system (1.1), then (u, v) must be (C1Uϵ, y, C2Uϵ, y) type with Morse index 1 and Morse index 2, where Uϵ, y is a positive ground state solution for a given equation.
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2020
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