# A singular System Involving the Fractional p-Laplacian Operator via the Nehari Manifold Approach

A singular System Involving the Fractional p-Laplacian Operator via the Nehari Manifold Approach Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0809-2 and Operator Theory A singular System Involving the Fractional p-Laplacian Operator via the Nehari Manifold Approach Kamel Saoudi Received: 24 December 2017 / Accepted: 28 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In this work we study the fractional p-Laplacian equation with singular nonlinearity s q−2 1−α −α 1−β ⎪ (−) u = λa(x )|u| u + c(x )|u| |v| , in , ⎪ p 2−α−β 1−β s q−2 1−α −β (−) v = μb(x )|v| v + c(x )|u| |v| , in , 2−α−β u = v = 0, in R \, ∗ ∗ N where 0 <α < 1, 0 <β < 1, 2−α −β< p < q < p , p = is the fractional s s N − ps Sobolev exponent, λ, μ are two parameters, a, b, c ∈ C () are non-negative weight functions with compact support in , and (−) is the fractional p-Laplace operator. We use the Nehari manifold approach and some variational techniques in order to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ and μ. Keywords http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Complex Analysis and Operator Theory Springer Journals

# A singular System Involving the Fractional p-Laplacian Operator via the Nehari Manifold Approach

, Volume OnlineFirst – Jun 4, 2018
18 pages

/lp/springer_journal/a-singular-system-involving-the-fractional-p-laplacian-operator-via-u5q1SDTRvB
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general; Operator Theory; Analysis
ISSN
1661-8254
eISSN
1661-8262
D.O.I.
10.1007/s11785-018-0809-2
Publisher site
See Article on Publisher Site

### Abstract

Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0809-2 and Operator Theory A singular System Involving the Fractional p-Laplacian Operator via the Nehari Manifold Approach Kamel Saoudi Received: 24 December 2017 / Accepted: 28 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In this work we study the fractional p-Laplacian equation with singular nonlinearity s q−2 1−α −α 1−β ⎪ (−) u = λa(x )|u| u + c(x )|u| |v| , in , ⎪ p 2−α−β 1−β s q−2 1−α −β (−) v = μb(x )|v| v + c(x )|u| |v| , in , 2−α−β u = v = 0, in R \, ∗ ∗ N where 0 <α < 1, 0 <β < 1, 2−α −β< p < q < p , p = is the fractional s s N − ps Sobolev exponent, λ, μ are two parameters, a, b, c ∈ C () are non-negative weight functions with compact support in , and (−) is the fractional p-Laplace operator. We use the Nehari manifold approach and some variational techniques in order to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ and μ. Keywords

### Journal

Complex Analysis and Operator TheorySpringer Journals

Published: Jun 4, 2018

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