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

Silvia Cingolani; Simone Secchi

doi:10.1017/S0308210513000450

Abstract

We prove the existence of positive ground state solutions to the pseudo-relativistic Schrödinger equation

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

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