Positive ground state solutions for fractional Laplacian system with one critical exponent and one subcritical exponent

2018/12/07 by Maoding Zhen, Zhen, Maoding, Jinchun He +5
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1812.02977

Abstract

In this paper, we consider the following fractional Laplacian system with one critical exponent and one subcritical exponent \begincases (-Δ)^su+μu=|u|^p-1u+λv amp; x∈ ℝ^N, (-Δ)^sv+νv = |v|^2^∗-2v+λuamp; x∈ ℝ^N,
\endcases where (-Δ)^s is the fractional Laplacian, 02s, λμ₀, there exists a λ_μ,ν∈[√(μ-μ₀)ν,√(μν)) such that if λ>λ_μ,ν, the system has a positive ground state solution, if λ

Citations

• The Brezis-Nirenberg result for the fractional Laplacian
• Regularity of the obstacle problem for a fractional power of the laplace operator

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