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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board Member: Armstrong, Scott N. / Astala, Kari / Colding, Tobias / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Finster, Felix / Gianazza, Ugo / Gursky, Matthew / Hardt, Robert / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / McCann, Robert / Mingione, Giuseppe / Nystrom, Kaj / Pacard, Frank / Preiss, David / Riviére, Tristan / Schaetzle, Reiner / Silvestre, Luis

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IMPACT FACTOR 2016: 1.182

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Volume 9, Issue 2 (Apr 2016)

Existence results for fractional p-Laplacian problems via Morse theory

Antonio Iannizzotto
  • Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Viale L. Merello 92, 09123 Cagliari, Italy
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/ Shibo Liu / Kanishka Perera
  • Department of Mathematical Sciences, Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901, USA
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/ Marco Squassina
Published Online: 2014-12-12 | DOI: https://doi.org/10.1515/acv-2014-0024


We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in the framework of continuum mechanics, phase transition phenomena, population dynamics and game theory. Under different growth assumptions on the reaction term, we obtain various existence as well as finite multiplicity results by means of variational and topological methods and, in particular, arguments from Morse theory.

Keywords: Fractional p-Laplacian problems; Morse theory; existence and multiplicity of weak solutions; regularity of solutions

MSC: 35P15; 35P30; 35R11

About the article

Received: 2014-07-17

Revised: 2014-10-22

Accepted: 2014-10-28

Published Online: 2014-12-12

Published in Print: 2016-04-01

Funding Source: GNAMPA

Award identifier / Grant number: Problemi al contorno per operatori non locali non lineari

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11171204

Funding Source: MIUR

Award identifier / Grant number: Variational and Topological Methods in the Study of Nonlinear Phenomena

Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2014-0024.

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