Ground states for the pseudo-relativistic Hartree equation with external potential

2014/02/26 by Silvia Cingolani, Cingolani, Silvia, Simone Secchi +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Quantum Chromodynamics and Particle Interactions #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1402.6479

In press

arxiv created 2014/02/26 · openalex publication_date 2014/02/26 · arxiv updated 2014/02/27 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We prove existence of positive ground state solutions to the pseudo-relativistic Schrödinger equation \ √(-Δ+m²) u +Vu = ( W * |u|^θ )|u|^θ-2 u \quadin ℝ^N
u ∈ H^1/2(ℝ^N) . where N ≥ 3, m >0, V is a bounded external scalar potential and W is a convolution potential, radially symmetric, satisfying suitable assumptions. We also furnish some asymptotic decay estimates of the found solutions.

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

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• On compact embeddings in L^p and fractional spaces

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