Bifurcation results for problems with fractional Trudinger-Moser nonlinearity

Kanishka Perera; Marco Squassina

doi:10.3934/dcdss.2018031

Article Contents

2018, Volume 11, Issue 3: 561-576. Doi: 10.3934/dcdss.2018031

This issue Previous Article Optimal elliptic regularity: A comparison between local and nonlocal equations Next Article

Bifurcation results for problems with fractional Trudinger-Moser nonlinearity

Kanishka Perera^1, and
Marco Squassina^2,

1.
Department of Mathematical Sciences, Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901, USA
2.
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia, Italy

Received: April 30, 2017

Revised: July 31, 2017

Published: June 2018

The second author is member of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Abstract

By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear fractional laplacian and a related critical exponential nonlinearity. This extends the literature for the $N$ -Laplacian operator.

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Mathematics Subject Classification: Primary: 35J92; Secondary: 35P30.

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References

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