Regularity of the lower positive branch for singular elliptic bifurcation problems
| dc.contributor.author | Godoy, Tomas | |
| dc.contributor.author | Guerin, Alfredo | |
| dc.date.accessioned | 2021-11-05T16:26:28Z | |
| dc.date.available | 2021-11-05T16:26:28Z | |
| dc.date.issued | 2019-04-12 | |
| dc.description.abstract | We consider the problem -∆u = αu-α + ƒ(λ, ∙, u) in Ω, u = 0 on ∂Ω, u > 0 in Ω, where Ω is a bounded domain in ℝn, λ ≥ 0, 0 ≤ α ∈ L∞(Ω), and 0 < α < 3. It is known that, under suitable assumptions on ƒ, there exists Λ > 0 such that this problem has at least one weak solution in H10(Ω) ∩ C(Ω̅) if and only if λ ∈ [0, Λ]; and that, for 0 < λ < Λ, at least two such solutions exist. Under additional hypothesis on α and ƒ, we prove regularity properties of the branch formed by the minimal weak solutions of the above problem. As a byproduct of the method used, we obtain the uniqueness of the positive solution when λ = Λ. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 32 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Godoy, T., & Guerin, A. (2019). Regularity of the lower positive branch for singular elliptic bifurcation problems. <i>Electronic Journal of Differential Equations, 2019</i>(49), pp. 1-32. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14782 | |
| 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 | singular elliptic problems | |
| dc.subject | positive solutions | |
| dc.subject | bifurcation problems | |
| dc.subject | implicit function theorem | |
| dc.subject | sub and super solutions | |
| dc.title | Regularity of the lower positive branch for singular elliptic bifurcation problems | |
| dc.type | Article |