Behaviour of Symmetric Solutions of a Nonlinear Elliptic Field Equation in the Semi-classical Limit: Concentration Around a Circle
| dc.contributor.author | D'Aprile, Teresa | |
| dc.date.accessioned | 2019-12-11T14:39:33Z | |
| dc.date.available | 2019-12-11T14:39:33Z | |
| dc.date.issued | 2000-11-16 | |
| dc.description.abstract | In this paper we study the existence of concentrated solutions of the nonlinear field equation -h2 ∆v + V(x)v - hp ∆pv + W' (v) = 0, where v : ℝN → ℝN+1, N ≥ 3, p > N, the potential V is positive and radial, and W is an appropriate singular function satisfying a suitable symmetric property. Provided that h is sufficiently small, we are able to find solutions with a certain spherical symmetry which exhibit a concentration behaviour near a circle centered at zero as h → 0+. Such solutions are obtained as critical points for the associated energy functional; the proofs of the results are variational and the arguments rely on topological tools. Furthermore a penalization-type method is developed for the identification of the desired solutions. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 40 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | D'Aprile, T. (2000). Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle. <i>Electronic Journal of Differential Equations, 2000</i>(69), pp. 1-40. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/9047 | |
| dc.language.iso | en | |
| dc.publisher | Southwest 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, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Nonlinear Schrodinger equations | |
| dc.subject | Topological charge | |
| dc.subject | Existence | |
| dc.subject | Concentration | |
| dc.title | Behaviour of Symmetric Solutions of a Nonlinear Elliptic Field Equation in the Semi-classical Limit: Concentration Around a Circle | |
| dc.type | Article |