A priori estimates for the Fractional p-Laplacian with nonlocal Neumann boundary conditions and applications

Dimitri Mugnai; Kanishka Perera; Edoardo Proietti Lippi

doi:10.3934/cpaa.2021177

Article Contents

2022, Volume 21, Issue 1: 275-292. Doi: 10.3934/cpaa.2021177

This issue Previous Article Variation operators for semigroups associated with Fourier-Bessel expansions Next Article Inverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation

A priori estimates for the Fractional p-Laplacian with nonlocal Neumann boundary conditions and applications

1.
Department of Ecology and Biology (DEB), Tuscia University, Largo dell'Università, 01100 Viterbo, Italy
2.
Department of Mathematical Sciences, Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901, USA
3.
Department of Mathematics and Computer Science, University of Florence, Viale Morgagni 67/A, 50134 Firenze - Italy

^* Corresponding author
^* Corresponding author

Received: August 2021

Revised: October 2021

Early access: October 2021

Published: January 2022

The first author is supported by the INdAM-GNAMPA Project 2020 "Equazioni alle derivate parziali: problemi e modelli" and by the FFABR "Fondo per il finanziamento delle attività base di ricerca" 2017

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Abstract

We first prove that solutions of fractional p-Laplacian problems with nonlocal Neumann boundary conditions are bounded and then we apply such a result to study some resonant problems by means of variational tools and Morse theory.

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Mathematics Subject Classification: Primary: 35R11, 58E05; Secondary: 35A15.

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References

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