Show simple item record

dc.contributor.authorYang, Yang ( )
dc.contributor.authorHong, Qian Yu ( )
dc.contributor.authorShang, Xudong ( )
dc.identifier.citationYang, Y., Hong, Q. Y., & Shang, X. (2019). Existence of solutions for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities. Electronic Journal of Differential Equations, 2019(90), pp. 1-32.en_US

In this work, we establish the existence of solutions for the non-linear nonlocal system of equations involving the fractional Laplacian,

(-∆)su = αu + bv + 2p / p+q ∫Ω |v(y)|q / |x-y|μ dy|u|p-2u
+2ξ1Ω |u(y)2*μ / |x-y|μ dy|u|2*μ-2u in Ω,
(-∆)sv = bu + cv + 2q / p+q ∫Ω |u(y)|p / |x-y|μ dy|v|q-2vv
+2ξ2Ω |v(y)2*μ / |x-y|μ dy|v|2*μ-2v in Ω,
u = v = 0 in ℝN \ Ω,

where (-∆)s is the fractional Laplacian operator, Ω is a smooth bounded domain in ℝN, 0 < s < 1, N > 2s, 0 < μ < N, ξ1, ξ2 ≥ 0, 1 < p, q ≤ 2*μ and 2*μ = 2N-μ / N-2s is the upper critical exponent in the Hardy-Littlewood-Sobolev inequality. The nonlinearities can interact with the spectrum of the fractional Laplacian. More specifically, the interval defined by the two eigenvalues of the real matrix from the linear part contains an eigenvalue of the spectrum of the fractional Laplacian. In this case, resonance phenomena can occur.

dc.format.extent32 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectFractional Laplacianen_US
dc.subjectChoquard equationen_US
dc.subjectLinking theoremen_US
dc.subjectHardy-Littlewood-Sobolev critical exponenten_US
dc.subjectMountain Pass theoremen_US
dc.titleExistence of solutions for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearitiesen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



This item appears in the following Collection(s)

Show simple item record