2020/11/19 by Gaetano Siciliano, Siciliano, Gaetano, Zhisu Liu +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.2011.09793
arxiv created 2020/11/19 · openalex publication_date 2020/11/19 · arxiv updated 2020/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the following Schrödinger-Born-infeld system with a general nonlinearity \ -\triangle u+u+ϕu=f(u)+μ|u|4u · in \R3,
-\textrmdiv((∇ϕ)/(√(1-|∇ϕ|2)))=u2 · in \R3,
u(x)→0, ϕ(x)→0, · as x→∞, . where μ≥0 and f∈ C(\R,\R) satisfies suitable assumptions. This system arises from a suitable coupling of the nonlinear Schrödinger equation and the Born-Infeld theory. We use a new perturbation approach to prove the existence and multiplicity of nontrivial solutions of the above system in the subcritical and critical case. We emphasise that our results cover the case f(u)=|u|p-1u for p∈(2,5/2] and μ=0 which was left in \citeAzzollini19 as an open problem.