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Forum Mathematicum

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Volume 30, Issue 1

Issues

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

-Δ+m2u+V(x)u=A(x)(W*|u|p)|u|p-2u

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

Keywords: Hartree equation; fractional Sobolev spaces

MSC 2010: 35J60; 35Q55; 35S05

Dedicated to Francesca, always

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About the article


Received: 2017-01-11

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, DOI: https://doi.org/10.1515/forum-2017-0006.

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