Existence of positive solutions for a class of fractional Choquard equation in exterior domain

César E. Torres Ledesma

doi:10.3934/dcds.2022016

Article Contents

2022, Volume 42, Issue 7: 3301-3328. Doi: 10.3934/dcds.2022016

This issue Previous Article Regularity of almost-minimizers of Hölder-coefficient surface energies Next Article Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without Ambrosetti-Rabinowitz condition

Existence of positive solutions for a class of fractional Choquard equation in exterior domain

César E. Torres Ledesma^,

Departamento de Matemáticas, Universidad Nacional de Trujillo, Av. Juan Pablo II s/n. Trujillo-Perú

^*Corresponding author: César E. Torres Ledesma
^*Corresponding author: César E. Torres Ledesma

Received: May 31, 2021

Revised: December 31, 2021

Published: July 2022

César T. Ledesma was partially supported by CONCYTEC, Peru, 379-2019-FONDECYT "ASPECTOS CUALITATIVOS DE ECUACIONES NO-LOCALES Y APLICACIONES"

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Abstract

In this paper we show existence of positive solutions for a class of problems involving the fractional Laplacian in exterior domain and Choquard type nonlinearity. We prove the main results using variational method combined with Brouwer theory of degree and Deformation Lemma..

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Mathematics Subject Classification: Primary: 35J60; Secondary: 35J65, 35Q55, 35R09.

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