Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schrodinger-Poisson system (SP): -Delta u+V(x)u+K(x)phi(x)u=u^5; -Delta phi =K(x)u^2 x in R^3. We remark that (SP) exhibits a ``double'' lack of compactness because of the unboundedness of R^3 and the critical growth of the nonlinear term and that in our assumptions ground state solutions of (SP) do not exist. "The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM "

Cerami, G., Molle, R. (2019). Multiple positive bound states for critical Schrödinger-Poisson systems. ESAIM. COCV, 25 [10.1051/cocv/2018071].

Multiple positive bound states for critical Schrödinger-Poisson systems

Molle R.
2019-01-01

Abstract

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schrodinger-Poisson system (SP): -Delta u+V(x)u+K(x)phi(x)u=u^5; -Delta phi =K(x)u^2 x in R^3. We remark that (SP) exhibits a ``double'' lack of compactness because of the unboundedness of R^3 and the critical growth of the nonlinear term and that in our assumptions ground state solutions of (SP) do not exist. "The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM "
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Schrodinger-Poisson system; lack of compactness; bund states; variational methods
The authors have been supported by the "Gruppo Nazionale per l'Analisi Matematica, la Probabilita' e le loro Applicazioni (GNAMPA)'' of the stituto Nazionale di Alta Matematica (INdAM) - Project: Sistemi differenziali ellittici nonlineari derivanti dallo studio di fenomeni elettromagnetici. The second author has been supported also by the research project: "Consolidate the Foundations: Nonlinear Differential Problems and their Applications'', of the University of Rome "Tor Vergata''.
https://arxiv.org/pdf/1802.02539.pdf
Cerami, G., Molle, R. (2019). Multiple positive bound states for critical Schrödinger-Poisson systems. ESAIM. COCV, 25 [10.1051/cocv/2018071].
Cerami, G; Molle, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/226343
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