Existence of solutions for a fractional elliptic problem with critical Sobolev-Hardy nonlinearities in R^N
| dc.contributor.author | Jin, Lingyu | |
| dc.contributor.author | Fang, Shaomei | |
| dc.date.accessioned | 2021-12-17T19:48:35Z | |
| dc.date.available | 2021-12-17T19:48:35Z | |
| dc.date.issued | 2018-01-10 | |
| dc.description.abstract | In this article, we study the fractional elliptic equation with critical Sobolev-Hardy nonlinearity (-∆)α u + α(x)u = |u|2*s - 2u/|x|s + k(x)|u|q-2u, u ∈ Hα (ℝN), where 2 < q < 2*, 0 < α < 1, N > 4α, 0 < s < 2α, 2*s = 2(N - s)/(N - 2α) is the critical Sobolev-Hardy exponent, 2* = 2N/(N - 2α) is the critical Sobolev exponent, α(x), k(x) ∈ C(ℝN). Through a compactness analysis of the functional associated, we obtain the existence of positive solutions under certain assumptions on α(x), k(x). | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 23 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Jin, L., & Fang, S. (2018). Existence of solutions for a fractional elliptic problem with critical Sobolev-Hardy nonlinearities in R^N. <i>Electronic Journal of Differential Equations, 2018</i>(12), pp. 1-23. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15067 | |
| 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, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional Laplacian | |
| dc.subject | Compactness | |
| dc.subject | Positive solution | |
| dc.subject | Unbounded domain | |
| dc.subject | Sobolev-Hardy nonlinearity | |
| dc.title | Existence of solutions for a fractional elliptic problem with critical Sobolev-Hardy nonlinearities in R^N | |
| dc.type | Article |