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Advances in Nonlinear Analysis

Editor-in-Chief: Radulescu, Vicentiu / Squassina, Marco

IMPACT FACTOR 2017: 4.674

CiteScore 2018: 5.03

SCImago Journal Rank (SJR) 2018: 3.215
Source Normalized Impact per Paper (SNIP) 2018: 3.225

Mathematical Citation Quotient (MCQ) 2017: 1.89

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Fractional elliptic equations with critical exponential nonlinearity

Jacques Giacomoni / Pawan Kumar Mishra / K. Sreenadh
Published Online: 2015-09-07 | DOI: https://doi.org/10.1515/anona-2015-0081


We study the existence of positive solutions for fractional elliptic equations of the type (-Δ)1/2u = h(u), u > 0 in (-1,1), u = 0 in ℝ∖(-1,1) where h is a real valued function that behaves like eu2 as u → ∞ . Here (-Δ)1/2 is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near t = 0. In case h is concave near t = 0, we show the existence of multiple solutions for suitable range of λ by analyzing the fibering maps and the corresponding Nehari manifold.

Keywords: Trudinger–Moser inequality; square root of laplacian; Nehari manifold

MSC: 35J20

About the article

Received: 2015-06-29

Revised: 2015-07-28

Accepted: 2015-08-04

Published Online: 2015-09-07

Published in Print: 2016-02-01

Citation Information: Advances in Nonlinear Analysis, Volume 5, Issue 1, Pages 57–74, ISSN (Online) 2191-950X, ISSN (Print) 2191-9496, DOI: https://doi.org/10.1515/anona-2015-0081.

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