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In this paper, we consider the following coupled Schrodinger system with critical exponent: −Δu=λu+|u|α−2u|v|β−1v,x∈Ω,−Δv=μ|v|2∗−2v+|u|α|v|β−1,x∈Ω,u,v>0,x∈Ω,u=v=0,x∈∂Ω, where Ω⊂RN(N≥3) is a smooth bounded domain, λ > 0,μ≥0, and α,β≥1,α+β=2∗=2NN−2. Under certain conditions on… Click to show full abstract
In this paper, we consider the following coupled Schrodinger system with critical exponent: −Δu=λu+|u|α−2u|v|β−1v,x∈Ω,−Δv=μ|v|2∗−2v+|u|α|v|β−1,x∈Ω,u,v>0,x∈Ω,u=v=0,x∈∂Ω, where Ω⊂RN(N≥3) is a smooth bounded domain, λ > 0,μ≥0, and α,β≥1,α+β=2∗=2NN−2. Under certain conditions on λ and μ, we show that this problem has at least one positive least energy solution. Copyright © 2016 John Wiley & Sons, Ltd.
Keywords:
positive least;
critical exponent;
least energy;
system critical
Journal Title: Mathematical Methods in The Applied Sciences
Year Published: 2017
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Journal Title: Mathematical Methods in The Applied Sciences
Year Published: 2017
Link to full text (if available)
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recommendations!