We prove the existence of positive ground state solutions to the pseudo-relativistic Schrödinger equation {equation presented}, where N ≥ 3, m > 0, V is a bounded external scalar potential and W is a radially symmetric convolution potential satisfying suitable assumptions. We also provide some asymptotic decay estimates of the found solutions.
Cingolani, S., Secchi, S. (2015). Ground states for the pseudo-relativistic Hartree equation with external potential. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 145(1), 73-90 [10.1017/S0308210513000450].
Ground states for the pseudo-relativistic Hartree equation with external potential
SECCHI, SIMONE
2015
Abstract
We prove the existence of positive ground state solutions to the pseudo-relativistic Schrödinger equation {equation presented}, where N ≥ 3, m > 0, V is a bounded external scalar potential and W is a radially symmetric convolution potential satisfying suitable assumptions. We also provide some asymptotic decay estimates of the found solutions.
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