Volume 25, 2019
|Number of page(s)||29|
|Published online||28 November 2019|
Multiple positive bound states for critical Schrödinger-Poisson systems
Dipartimento di Matematica, Politecnico di Bari,
Via Amendola 126/B,
2 Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica no 1, 00133 Roma, Italy.
* Corresponding author: firstname.lastname@example.org
Accepted: 8 December 2018
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.
Mathematics Subject Classification: 35J20 / 35J60
Key words: Schrödinger-Poisson system / lack of compactness / bound states / variational methods
© EDP Sciences, SMAI 2019
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