First curve of Fucik spectrum for the p-fractional Laplacian operator with nonlocal normal boundary conditions
| dc.contributor.author | Goel, Divya | |
| dc.contributor.author | Goyal, Sarika | |
| dc.contributor.author | Sreenadh, Konijeti | |
| dc.date.accessioned | 2022-01-26T19:45:05Z | |
| dc.date.available | 2022-01-26T19:45:05Z | |
| dc.date.issued | 2018-03-17 | |
| dc.description.abstract | In this article, we study the Fučik spectrum of the p-fractional Laplace operator with nonlocal normal derivative conditions which is defined as the set of all (α, b) ∈ ℝ2 such that ∧n,p (1 - α) (-∆)αpu + |u|p-2u = XΩε/ε (α(u+)p-1 -b(uˉ)p-1) in Ω, Nα,pu = 0 in ℝn \ Ω̅, has a non-trivial solution u, where Ω is a bounded domain in ℝn with Lipschitz boundary, p ≥ 2, n > pα, ε, α ∈ (0, 1) and Ωε ≔ {x ∈ Ω : d(x, ∂Ω) ≤ ε}. We show existence of the first non-trivial curve C of the Fučik spectrum which is used to obtain the variational characterization of a second eigenvalue of the problem defined above. We also discuss some properties of this curve C, e.g., Lipschitz continuous, strictly decreasing and asymptotic behavior and non-resonance with respect to the Fučik spectrum. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Goel, D., Goyal, S., & Sreenadh, K. (2018). First curve of Fucik spectrum for the p-fractional Laplacian operator with nonlocal normal boundary conditions. <i>Electronic Journal of Differential Equations, 2018</i>(74), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15216 | |
| 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 | Nonlocal operator | |
| dc.subject | Fucik spectrum | |
| dc.subject | Steklov problem | |
| dc.subject | Non-resonance | |
| dc.title | First curve of Fucik spectrum for the p-fractional Laplacian operator with nonlocal normal boundary conditions | |
| dc.type | Article |