Normalized solutions for a class of nonlinear Choquard equations

We prove the existence of a least energy solution to the problem - Δ u - ( I α ∗ F ( u ) ) f ( u ) = λ u in R N , ∫ R N u 2 ( x ) d x = a 2 , where N ≥ 1 , α ∈ ( 0 , N ) , F ( s ) : = ∫ 0 s f ( t ) d t , and I α : R N → R is the Riesz potential. If f is odd in u then we prove the existence of infini...

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Bibliographic Details
Published in:SN partial differential equations and applications 2020-10, Vol.1 (5), Article 34
Main Authors: Bartsch, Thomas, Liu, Yanyan, Liu, Zhaoli
Format: Article
Language:English
Subjects:
Analysis
Mathematical and Computational Biology
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
On the Occasion of Prof. Dajun Guo’s 85th Birthday
Original Paper
Partial Differential Equations
Theoretical
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Summary:We prove the existence of a least energy solution to the problem - Δ u - ( I α ∗ F ( u ) ) f ( u ) = λ u in R N , ∫ R N u 2 ( x ) d x = a 2 , where N ≥ 1 , α ∈ ( 0 , N ) , F ( s ) : = ∫ 0 s f ( t ) d t , and I α : R N → R is the Riesz potential. If f is odd in u then we prove the existence of infinitely many normalized solutions.
ISSN:2662-2963
2662-2971
DOI:10.1007/s42985-020-00036-w