Existence of standing waves for Schrodinger equations involving the fractional Laplacian
| dc.contributor.author | de Medeiros, Everaldo S. | |
| dc.contributor.author | Cardoso, Jose Anderson | |
| dc.contributor.author | de Souza, Manasses | |
| dc.date.accessioned | 2022-04-04T20:51:03Z | |
| dc.date.available | 2022-04-04T20:51:03Z | |
| dc.date.issued | 2017-03-20 | |
| dc.description.abstract | We study a class of fractional Schrödinger equations of the form ε2α(-∆)α u + V(x)u = ƒ(x, u) in ℝN, where ε is a positive parameter, 0 < α < 1, 2α < N, (-∆)α is the fractional Laplacian, V : ℝN → ℝ is a potential which may be bounded or unbounded and the nonlinearity ƒ : ℝN x ℝ → ℝ is superlinear and behaves like |u|p-2 u at infinity for some 2 < p < 2*α ≔ 2N / (N - 2α). Here we use a variational approach based on the Caffarelli and Silvestre's extension developed in [3] to obtain a nontrivial solution for ε sufficiently small. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | de Medeiros, E. S., Cardoso, J. A., & de Souza, M. (2017). Existence of standing waves for Schrodinger equations involving the fractional Laplacian. <i>Electronic Journal of Differential Equations, 2017</i>(76), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15603 | |
| 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, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Variational methods | |
| dc.subject | Critical points | |
| dc.subject | Fractional Laplacian | |
| dc.title | Existence of standing waves for Schrodinger equations involving the fractional Laplacian | |
| dc.type | Article |