Geodesic
Multiple positive bound states for critical Schrödinger-Poisson systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 73.

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Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schrödinger-Poisson system: $$

We remark that (SP) exhibits a “double” lack of compactness because of the unboundedness of ℝ3 and the critical growth of the nonlinear term and that in our assumptions ground state solutions of (SP) do not exist.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018071
Classification : 35J20, 35J60
Keywords: Schrödinger-Poisson system, lack of compactness, bound states, variational methods

Cerami, Giovanna 1 ; Molle, Riccardo 1

1 
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Cerami, Giovanna; Molle, Riccardo. Multiple positive bound states for critical Schrödinger-Poisson systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 73. doi : 10.1051/cocv/2018071. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018071/

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