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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  and
Simone Secchi
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)
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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.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 1 , February 2015 , pp. 73 - 90
Copyright
Copyright © Royal Society of Edinburgh 2015 

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