The Nehari manifold for fractional systems involving critical nonlinearities

Xiaoming He; Marco Squassina; Wenming Zou

doi:10.3934/cpaa.2016.15.1285

The Nehari manifold for fractional systems involving critical nonlinearities

Xiaoming He, Marco Squassina, Wenming Zou

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters (λ, µ) belongs to a suitable subset of R^2

Original language	English
Pages (from-to)	1285-1308
Number of pages	24
Journal	Communications on Pure and Applied Analysis
Volume	15
DOIs	https://doi.org/10.3934/cpaa.2016.15.1285
Publication status	Published - 2016

Keywords

Fractional systems
Nehari manifold technique

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10.3934/cpaa.2016.15.1285

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title = "The Nehari manifold for fractional systems involving critical nonlinearities",

abstract = "We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters (λ, µ) belongs to a suitable subset of R^2",

keywords = "Fractional systems, Nehari manifold technique, Fractional systems, Nehari manifold technique",

author = "Xiaoming He and Marco Squassina and Wenming Zou",

year = "2016",

doi = "10.3934/cpaa.2016.15.1285",

language = "English",

volume = "15",

pages = "1285--1308",

journal = "Communications on Pure and Applied Analysis",

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publisher = "American Institute of Mathematical Sciences",

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T1 - The Nehari manifold for fractional systems involving critical nonlinearities

AU - He, Xiaoming

AU - Squassina, Marco

AU - Zou, Wenming

PY - 2016

Y1 - 2016

N2 - We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters (λ, µ) belongs to a suitable subset of R^2

AB - We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters (λ, µ) belongs to a suitable subset of R^2

KW - Fractional systems

KW - Nehari manifold technique

KW - Fractional systems

KW - Nehari manifold technique

UR - http://hdl.handle.net/10807/87016

U2 - 10.3934/cpaa.2016.15.1285

DO - 10.3934/cpaa.2016.15.1285

M3 - Article

SN - 1534-0392

VL - 15

SP - 1285

EP - 1308

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

ER -

The Nehari manifold for fractional systems involving critical nonlinearities

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Keywords

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