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EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO EIGENVALUE PROBLEMS FOR SCHRÓDINGER-BOPP-PODOLSKY EQUATIONS

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Autor(es):
Hernandez, Lorena Soriano ; Siciliano, Gaetano
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: Electronic Journal of Differential Equations; v. 2023, n. 66, p. 18-pg., 2023-10-13.
Resumo

We study the existence and multiplicity of solutions for the Schrodinger-Bopp-Podolsky system -Delta u + phi u = omega u in Omega alpha 2 Delta 2 phi - Delta phi = u(2) in Omega u = phi = Delta phi = 0 on partial derivative Omega integral(Omega)u(2) dx = 1 where Omega is an open bounded and smooth domain in R-3 , a > 0 is the Bopp-Podolsky parameter. The unknowns are u, phi : Omega -> R and omega is an element of 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. (AU)

Processo FAPESP: 22/16407-1 - TESEd: Temático em Equações e Sistemas de Equações diferenciais
Beneficiário:Ederson Moreira dos Santos
Modalidade de apoio: Auxílio à Pesquisa - Temático