Positive solution for Hénon type equations with critical Sobolev growth
| dc.contributor.author | Takahashi, Kazune | |
| dc.date.accessioned | 2022-03-10T20:50:22Z | |
| dc.date.available | 2022-03-10T20:50:22Z | |
| dc.date.issued | 2018-11-28 | |
| dc.description.abstract | We investigate the Hénon type equation involving the critical Sobolev exponent with Dirichret boundary condition -∆u = λΨu + |x|α u2*-1 in Ω included in a unit ball, under several conditions. Here, Ψ is a non-trivial given function with 0 ≤ Ψ ≤ 1 which may vanish on ∂Ω. Let λ1 be the first eigenvalue of the Dirichret eigenvalue problem -∆φ = λΨφ in Ω. We show that if the dimension N ≥ 4 and 0 < λ < λ1, there exists a positive solution for small α > 0. Our methods include the mountain pass theorem and the Talenti function. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Takahashi, K. (2018). Positive solution for Hénon type equations with critical Sobolev growth. <i>Electronic Journal of Differential Equations, 2018</i>(194), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15490 | |
| 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 | Critical Sobolev exponent | |
| dc.subject | Henon equation | |
| dc.subject | Mountain Pass Theorem | |
| dc.subject | Talenti function | |
| dc.title | Positive solution for Hénon type equations with critical Sobolev growth | |
| dc.type | Article |