Existence of solutions for nonlinear Dirac equations in the Bopp-Podolsky electrodynamics

2023/05/09 by Hlel Missaoui, Missaoui, Hlel
Mathematics · Physics and Astronomy · #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2305.05483

Abstract

In this paper, we study the following nonlinear Dirac-Bopp-Podolsky system \lbrace -i∑_k=1³α_k∂_ku+[V(x)+q]βu+wu-ϕu · amp;=f(x,u), · amp;in ℝ³, · amp; · amp; -\triangleϕ+a²\triangle² ϕ · amp;=4π\vert u\vert², · amp; in ℝ³, . where a,q>0,w∈ ℝ, V(x) is a potential function, and f(x, u) is the interaction term (nonlinearity). First, we give a physical motivation for this new kind of system. Second, under suitable assumptions on f and V, and by means of minimax techniques involving Cerami sequences, we prove the existence of at least one pair of solutions (u,ϕ_u).

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