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

Published online by Cambridge University Press:  30 January 2015

Silvia Cingolani
Affiliation:
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy, (silvia.cingolani@poliba.it)
Simone Secchi
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via R. Cozzi 55, 20125 Milan, Italy, (simone.secchi@unimib.it)

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2015 

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