Existence of multiple solutions to Schrödinger–Poisson system in a nonlocal set up in R3

The aim of this work is to study the following system: ( - Δ ) s u + α ϕ u = β u - γ + g ( u ) + h ( x ) in R 3 u > 0 in R 3 ( - Δ ) s ϕ = u 2 in R 3 . under the Berestycki–Lions type condition. Here α , β > 0 , 0 < s , γ < 1 , g ∈ C ( R , R ) , h ∈ L 2 ( R 3 ) . We will prove the existe...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2022, Vol.73 (1)
Main Authors: Choudhuri, Debajyoti, Saoudi, Kamel
Format: Article
Language:English
Subjects:
Engineering
Mathematical Methods in Physics
Mountains
Theoretical and Applied Mechanics
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Summary:The aim of this work is to study the following system: ( - Δ ) s u + α ϕ u = β u - γ + g ( u ) + h ( x ) in R 3 u > 0 in R 3 ( - Δ ) s ϕ = u 2 in R 3 . under the Berestycki–Lions type condition. Here α , β > 0 , 0 < s , γ < 1 , g ∈ C ( R , R ) , h ∈ L 2 ( R 3 ) . We will prove the existence of at least two solutions using the Ekeland’s variational principle, Mountain pass theorem and a Pohožaev type identity.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-021-01649-w