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Keywords = Schwarz symmetry rearrangement

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15 pages, 285 KiB  
Article
Radial Symmetry for Weak Positive Solutions of Fractional Laplacian with a Singular Nonlinearity
by Xing Wang and Li Zhang
Symmetry 2018, 10(12), 695; https://doi.org/10.3390/sym10120695 - 3 Dec 2018
Viewed by 2752
Abstract
This paper is concerned with the radial symmetry weak positive solutions for a class of singular fractional Laplacian. The main results in the paper demonstrate the existence and multiplicity of radial symmetry weak positive solutions by Schwarz spherical rearrangement, constrained minimization, and Ekeland’s [...] Read more.
This paper is concerned with the radial symmetry weak positive solutions for a class of singular fractional Laplacian. The main results in the paper demonstrate the existence and multiplicity of radial symmetry weak positive solutions by Schwarz spherical rearrangement, constrained minimization, and Ekeland’s variational principle. It is worth pointing out that our results extend the previous works of T. Mukherjee and K. Sreenadh to a setting in which the testing functions need not have a compact support. Moreover, we weakened one of the conditions used in their papers. Our results improve on existing studies on radial symmetry solutions of nonlocal boundary value problems. Full article
(This article belongs to the Special Issue Fixed Point Theory and Fractional Calculus with Applications)
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