Existence of solutions for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities
| dc.contributor.author | Yang, Yang | |
| dc.contributor.author | Hong, Qian Yu | |
| dc.contributor.author | Shang, Xudong | |
| dc.date.accessioned | 2021-11-29T21:03:25Z | |
| dc.date.available | 2021-11-29T21:03:25Z | |
| dc.date.issued | 2019-07-19 | |
| dc.description.abstract | 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 +2ξ1 ∫Ω |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 +2ξ2 ∫Ω |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.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 32 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Yang, Y., Hong, Q. Y., & Shang, X. (2019). Existence of solutions for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities. <i>Electronic Journal of Differential Equations, 2019</i>(90), pp. 1-32. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14978 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional Laplacian | |
| dc.subject | Choquard equation | |
| dc.subject | Linking theorem | |
| dc.subject | Hardy-Littlewood-Sobolev critical exponent | |
| dc.subject | Mountain Pass theorem | |
| dc.title | Existence of solutions for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities | |
| dc.type | Article |