Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition
| dc.contributor.author | Repovs, Dusan D. | |
| dc.date.accessioned | 2022-01-07T16:55:34Z | |
| dc.date.available | 2022-01-07T16:55:34Z | |
| dc.date.issued | 2018-02-06 | |
| dc.description.abstract | We study the degenerate elliptic equation -div(|x|α∇u) = ƒ(u) + tφ(x) + h(x) in a bounded open set Ω with homogeneous Neumann boundary condition, where α ∈ (0, 2) and ƒ has a linear growth. The main result establishes the existence of real numbers t* and t* such that the problem has at least two solutions if t ≤ t*, there is at least one solution if t* < t ≤ t*, and no solution exists for all t > t*. The proof combines a priori estimates with topological degree arguments. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Repovs, D. D. (2018). Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition. <i>Electronic Journal of Differential Equations, 2018</i>(41), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15097 | |
| 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 | Ambrosetti-Prodi problem | |
| dc.subject | Degenerate potential | |
| dc.subject | Topological degree | |
| dc.subject | Anisotropic continuous media | |
| dc.title | Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition | |
| dc.type | Article |