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Licensed Unlicensed Requires Authentication Published by De Gruyter December 12, 2014

Existence results for fractional p-Laplacian problems via Morse theory

Antonio Iannizzotto, Shibo Liu, Kanishka Perera and Marco Squassina

Abstract

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.

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

The authors would like to thank Xavier Ros-Oton for precious bibliographic information on the regularity up to the boundary of the solutions to the problem, as well as Sun-Ra Mosconi for some useful remarks concerning Section 5.

Received: 2014-7-17
Revised: 2014-10-22
Accepted: 2014-10-28
Published Online: 2014-12-12
Published in Print: 2016-4-1

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