Nontrivial complex solutions for magnetic Schrodinger equations with critical nonlinearities
| dc.contributor.author | Barile, Sara | |
| dc.contributor.author | Figueiredo, Giovany M. | |
| dc.date.accessioned | 2022-03-09T20:48:06Z | |
| dc.date.available | 2022-03-09T20:48:06Z | |
| dc.date.issued | 2018-10-22 | |
| dc.description.abstract | Using minimization arguments we establish the existence of a complex solution to the magnetic Schrödinger equation -(∇ + iA(x))2u + u = ƒ(|u|2)u in ℝN, where N ≥ 3, A:ℝN → ℝN is the magnetic potential and ƒ satisfies some critical growth assumptions. First we obtain bounds from a real Pohozaev manifold. Then relate them to Sobolev imbedding constants and to the least energy level associated with the real equation in absence of the magnetic field (i.e., with A(x) = 0). We also apply the Lions Concentration Compactness Principle to the modula of the minimizing sequences involved. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Barile, S., & Figueiredo, G. M. (2018). Nontrivial complex solutions for magnetic Schrodinger equations with critical nonlinearities. <i>Electronic Journal of Differential Equations, 2018</i>(174), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15470 | |
| 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 | Magnetic Schrödinger equations | |
| dc.subject | Critical nonlinearities | |
| dc.subject | Minimization problem | |
| dc.subject | Concentration-compactness methods | |
| dc.subject | Pohozaev manifold | |
| dc.title | Nontrivial complex solutions for magnetic Schrodinger equations with critical nonlinearities | |
| dc.type | Article |