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- Title
EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO EIGENVALUE PROBLEMS FOR SCHRODINGER-BOPP-PODOLSKY EQUATIONS.
- Authors
HERNANDEZ, LORENA SORIANO; SICILIANO, GAETANO
- Abstract
We study the existence and multiplicity of solutions for the Schrodinger-Bopp-Podolsky system - Δ u + ϕ u = ω u in Ω a 2 Δ 2 ϕ - Δ ϕ = u 2 in Ω u = ϕ = Δ ϕ = 0 on ∂ Ω ∫ Ω u 2 d x = 1 where Ω is an open bounded and smooth domain in R 3, a > 0 is the Bopp-Podolsky parameter. The unknowns are u, ϕ: Ω → R and ω ∈ R. By using variational methods we show that for any a > 0 there are infinitely many solutions with diverging energy and divergent in norm. We show that ground states solutions converge to a ground state solution of the related classical Schrodinger-Poisson system, as a → 0.
- Publication
Electronic Journal of Differential Equations, 2023, Issue 74, p1
- ISSN
1550-6150
- Publication type
Article
- DOI
10.58997/ejde.2023.66