Nonlinear perturbations of a periodic fractional Laplacian with supercritical growth
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Published:2021-09-12
Issue:
Volume:
Page:335-349
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Author:
Figueiredo Giovany M.ORCID,
Moreira Sandra I.,
Ruviaro RicardoORCID
Abstract
Our main goal is to explore the existence of positive solutions for a class of nonlinear fractional Schrödinger equation involving supercritical growth given by $$ (- \Delta)^{\alpha} u + V(x)u=p(u),\quad x\in \mathbb{R^N},\ N \geq 1. $$ We analyze two types of problems, with $V$ being periodic and asymptotically periodic; for this we use a variational method, a truncation argument and a concentration compactness principle.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis