An Elliptic Equation with Spike Solutions Concentrating at Local Minima of the Laplacian of the Potential
| dc.contributor.author | Spradlin, Gregory S. | |
| dc.date.accessioned | 2020-01-07T16:23:48Z | |
| dc.date.available | 2020-01-07T16:23:48Z | |
| dc.date.issued | 2000-05-02 | |
| dc.description.abstract | We consider the equation -∈² ∆u + V(z)u = ƒ(u) which arises in the study of nonlinear Schrödinger equations. We seek solutions that are positive on ℝN and that vanish at infinity. Under the assumption that ƒ satisfies super-linear and sub-critical growth conditions, we show that for small ∊ there exist solutions that concentrate near local minima of V. The local minima may occur in unbounded components, as long as the Laplacian of V achieves a strict local minimum along such a component. Our proofs employ variational mountain-pass and concentration compactness arguments. A penalization technique developed by Felmer and del Pino is used to handle the lack of compactness and the absence of the Palais-Smale condition in the variational framework. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 14 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Spradlin, G. S. (2000). An elliptic equation with spike solutions concentrating at local minima of the Laplacian of the potential. <i>Electronic Journal of Differential Equations, 2000</i>(32), pp. 1-14. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/9142 | |
| 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 equation | |
| dc.subject | Variational methods | |
| dc.subject | Singularly perturbed elliptic equation | |
| dc.subject | Mountain-pass theorem | |
| dc.subject | Concentration compactness | |
| dc.subject | Degenerate critical points | |
| dc.title | An Elliptic Equation with Spike Solutions Concentrating at Local Minima of the Laplacian of the Potential | en_US |
| dc.type | Article |