We study the existence and multiplicity of solutions for the Schrödinger-Bopp-Podolsky system (formula presented) where Ω is an open bounded and smooth domain in R3, 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 Schrödinger-Poisson system, as a → 0.
EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO EIGENVALUE PROBLEMS FOR SCHRÖDINGER-BOPP-PODOLSKY EQUATIONS
Siciliano G.
2023-01-01
Abstract
We study the existence and multiplicity of solutions for the Schrödinger-Bopp-Podolsky system (formula presented) where Ω is an open bounded and smooth domain in R3, 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 Schrödinger-Poisson system, as a → 0.File in questo prodotto:
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