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2021 Nonlinear perturbations of a periodic fractional Laplacian with supercritical growth
Giovany M. Figueiredo, Sandra I. Moreira, Ricardo Ruviaro
Topol. Methods Nonlinear Anal. 58(1): 335-349 (2021). DOI: 10.12775/TMNA.2020.073

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.

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Giovany M. Figueiredo. Sandra I. Moreira. Ricardo Ruviaro. "Nonlinear perturbations of a periodic fractional Laplacian with supercritical growth." Topol. Methods Nonlinear Anal. 58 (1) 335 - 349, 2021. https://doi.org/10.12775/TMNA.2020.073

Information

Published: 2021
First available in Project Euclid: 21 September 2021

Digital Object Identifier: 10.12775/TMNA.2020.073

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.58 • No. 1 • 2021
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