Profile of solutions for nonlocal equations with critical and supercritical nonlinearities-Reference-Cited by-同舟云学术

Profile of solutions for nonlocal equations with critical and supercritical nonlinearities

Published:2019-01-28 Issue:01 Volume:21 Page:1750099
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Bhakta Mousomi¹,Mukherjee Debangana¹,Santra Sanjiban²

Affiliation:

1. Department of Mathematics, Indian Institute of Science Education and Research, Dr. Homi Bhaba Road, Pune 411008, India

2. Department of Basic Mathematics, Centro de Investigacióne en Mathematicás, Guanajuato, México

Abstract

We study the fractional Laplacian problem [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] is a parameter. Here, [Formula: see text] is a bounded star-shaped domain with smooth boundary and [Formula: see text]. We establish existence of a variational positive solution [Formula: see text] and characterize the asymptotic behavior of [Formula: see text] as [Formula: see text]. When [Formula: see text], we describe how the solution [Formula: see text] blows up at an interior point of [Formula: see text]. Furthermore, we prove the local uniqueness of solution of the above problem when [Formula: see text] is a convex symmetric domain of [Formula: see text] with [Formula: see text] and [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199717500997

Reference35 articles.

1. Large $s$-harmonic functions and boundary blow-up solutions for the fractional Laplacian

2. A critical fractional equation with concave–convex power nonlinearities

3. Nonlinear scalar field equations, I existence of a ground state

4. Semilinear nonlocal elliptic equations with critical and supercritical exponents

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