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arXiv · 2309.01841

Concentrated solutions to the Schrödinger--Bopp--Podolsky system with a positive potential

Gustavo de Paula Ramos
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Abstract

Consider the Schrödinger--Bopp--Podolsky system \[ \begin{cases} -ε^2Δu+(V+Kϕ)u=u|u|^{p-1};\newline Δ^2ϕ-Δϕ=4πK u^2 \end{cases} ~\text{in}~\mathbb{R}^3 \] for sufficiently small $ε>0$, where $V,K\colon\mathbb{R}^3\to [0,\infty[$; $p\in ]1,5[$ are fixed and we want to solve for $u,ϕ\colon\mathbb{R}^3\to\mathbb{R}$. Under certain hypotheses, we estimate the multiplicity of solutions in function of a critical manifold of $V$ and we establish the existence of solutions concentrated around critical points of $V$.

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Gustavo de Paula Ramos. 2023-09-04. Concentrated solutions to the Schrödinger--Bopp--Podolsky system with a positive potential. https://doi.org/10.1016/j.jmaa.2024.128098

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