Journal article 582 views 46 downloads
Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems
Tomas Dutko,
Carlo Mercuri,
Megan Tyler
Calculus of Variations and Partial Differential Equations, Volume: 60, Issue: 5
Swansea University Authors: Carlo Mercuri, Megan Tyler
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DOI (Published version): 10.1007/s00526-021-02045-y
Abstract
We study a nonlinear Schrödinger-Poisson system which reduces to a nonlinear andnonlocal PDE set on the whole spatial domain, whose variational formulation requires propertiesof a suitable finite energy space, such as separability and compactness, that we study and use.Our equation involves a weight...
| Published in: | Calculus of Variations and Partial Differential Equations |
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| ISSN: | 0944-2669 1432-0835 |
| Published: |
Springer Science and Business Media LLC
2021
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa57454 |
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| Abstract: |
We study a nonlinear Schrödinger-Poisson system which reduces to a nonlinear andnonlocal PDE set on the whole spatial domain, whose variational formulation requires propertiesof a suitable finite energy space, such as separability and compactness, that we study and use.Our equation involves a weight function which is allowed as particular scenarios, to either 1) vanish on a region and be finite at infinity, or 2) be large at infinity. We find least energy solutionsin both cases, studying the vanishing case by means of a priori integral bounds on sequences ofapproximating solutions and highlighting the role of certain positive universal constants for thesebounds to hold. Within the Ljusternik-Schnirelman theory we show the existence of infinitelymany distinct pairs of high energy solutions, having a min-max characterisation given by meansof the Krasnoselskii genus. |
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| Keywords: |
Nonlinear Schrödinger–Poisson system; Weighted Sobolev spaces; Palais–Smale sequences; Compactness; Multiple solutions; Nonexistence |
| College: |
Faculty of Science and Engineering |
| Issue: |
5 |