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dc.contributor.authorSpradlin, Gregory S. ( )
dc.date.accessioned2020-01-07T16:23:48Z
dc.date.available2020-01-07T16:23:48Z
dc.date.issued2000-05-02
dc.identifier.citationSpradlin, G. S. (2000). An elliptic equation with spike solutions concentrating at local minima of the Laplacian of the potential. Electronic Journal of Differential Equations, 2000(32), pp. 1-14.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/9142
dc.description.abstractWe 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.en_US
dc.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNonlinear Schrodinger equationen_US
dc.subjectVariational methodsen_US
dc.subjectSingularly perturbed elliptic equationen_US
dc.subjectMountain-pass theoremen_US
dc.subjectConcentration compactnessen_US
dc.subjectDegenerate critical pointsen_US
dc.titleAn Elliptic Equation with Spike Solutions Concentrating at Local Minima of the Laplacian of the Potentialen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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