Monotonicity properties of the eigenvalues of nonlocal fractional operators and their applications
| dc.contributor.author | Molica Bisci, Giovanni | |
| dc.contributor.author | Servadei, Raffaella | |
| dc.contributor.author | Zhang, Binlin | |
| dc.date.accessioned | 2023-05-15T20:55:32Z | |
| dc.date.available | 2023-05-15T20:55:32Z | |
| dc.date.issued | 2022-12-21 | |
| dc.description.abstract | In this article we study an equation driven by the nonlocal integrodifferential operator -LK in presence of an asymmetric nonlinear term f. Among the main results of the paper we prove the existence of at least a weak solution for this problem, under suitable assumptions on the asymptotic behavior of the nonlinearity f at ±∞. Moreover, we show the uniqueness of this solution, under additional requirements on f. We also give a non-existence result for the problem under consideration. All these results were obtained using variational techniques and a monotonicity property of the eigenvalues of -LK with respect to suitable weights, that we prove along the present paper. This monotonicity property is of independent interest and represents the nonlocal counterpart of a famous result obtained by de Figueiredo and Gossez [14] in the setting of uniformly elliptic operators. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Molica Bisci, G., Servadei, R., & Zhang, B. (2022). Monotonicity properties of the eigenvalues of nonlocal fractional operators and their applications. Electronic Journal of Differential Equations, 2022(85), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16809 | |
| 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, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional Laplacian | |
| dc.subject | Integrodifferential operator | |
| dc.subject | Nonlocal problems | |
| dc.subject | Eigenvalue and eigenfunction | |
| dc.subject | Asymmetric nonlinearities | |
| dc.subject | Variational methods | |
| dc.subject | Critical point theory | |
| dc.subject | Saddle point theorem | |
| dc.title | Monotonicity properties of the eigenvalues of nonlocal fractional operators and their applications | |
| dc.type | Article |