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On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
Carlo Mercuri,
Megan Tyler
Revista Matemática Iberoamericana
Swansea University Authors: Carlo Mercuri, Megan Tyler
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DOI (Published version): 10.4171/rmi/1158
Abstract
In the spirit of the classical work of P. H. Rabinowitz on nonlinear Schrödinger equations, we prove existence of mountain-pass solutions and least energy solutions to a class of nonlinear Schrödinger-Poisson systems under different assumptions on a weight function at infinity. Our results cover a r...
| Published in: | Revista Matemática Iberoamericana |
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| ISSN: | 0213-2230 |
| Published: |
European Mathematical Society Publishing House
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa44664 |
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| Abstract: |
In the spirit of the classical work of P. H. Rabinowitz on nonlinear Schrödinger equations, we prove existence of mountain-pass solutions and least energy solutions to a class of nonlinear Schrödinger-Poisson systems under different assumptions on a weight function at infinity. Our results cover a range of exponents, p,where the lack of compactness phenomena may be due to the combined effect of the invariance by translations of a `limiting problem' at infinity and of the possible unboundedness of the Palais-Smale sequences. Moreover, we find necessary conditions for concentration at points to occur for solutions to a singular perturbation of the same problem in various functional settings which are suitable for both variational and perturbation methods. |
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| Keywords: |
Stationary Nonlinear Schrödinger-Poisson System, Weighted Sobolev Spaces, Palais-Smale Sequences, Lack of Compactness. |
| College: |
Faculty of Science and Engineering |