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

2014/02/26 by Silvia Cingolani, Cingolani, Silvia, Simone Secchi +1
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

paper · pdf · doi:10.48550/arxiv.1402.6479

openalex publication_date 2014/02/26 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We prove existence of positive ground state solutions to the\npseudo-relativistic Schr "odinger equation \
left
\n√(-
Delta +m²) u +Vu =
left( W * |u|
^theta\n
right)|u|
^{theta -2} u
quad
textin
mathbbR^N

u
in\nH^1/2(
mathbbR^N) \
right. where N \≥ 3, m\n>0, V is a bounded external scalar potential and W is a convolution\npotential, radially symmetric, satisfying suitable assumptions. We also furnish\nsome asymptotic decay estimates of the found solutions.\n

Citations

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

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