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# Forum Mathematicum

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Volume 30, Issue 1

# Existence of solutions for a semirelativistic Hartree equation with unbounded potentials

Simone Secchi
• Corresponding author
• Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, via Cozzi 55, 20125 Milano, Italy
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Published Online: 2017-04-20 | DOI: https://doi.org/10.1515/forum-2017-0006

## Abstract

We prove the existence of a solution to the semirelativistic Hartree equation

$\sqrt{-\mathrm{\Delta }+{m}^{2}}u+V\left(x\right)u=A\left(x\right)\left(W*{|u|}^{p}\right){|u|}^{p-2}u$

under suitable growth assumption on the potential functions V and A. In particular, both can be unbounded from above.

MSC 2010: 35J60; 35Q55; 35S05

Dedicated to Francesca, always

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Published Online: 2017-04-20

Published in Print: 2018-01-01

The author is supported by the MIUR 2015 PRIN project “Variational methods, with applications to problems in mathematical physics and geometry”.

Citation Information: Forum Mathematicum, Volume 30, Issue 1, Pages 129–140, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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