Existence results for a fractional elliptic system with critical Sobolev-Hardy exponents and concave-convex nonlinearities

Jinguo Zhang; Tsing San Hsu

doi:10.1002/mma.6134

Existence results for a fractional elliptic system with critical Sobolev-Hardy exponents and concave-convex nonlinearities

Jinguo Zhang^*
, Tsing San Hsu

^*Corresponding author for this work

Center for General Education

Jiangxi Normal University

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

3 Scopus citations

Abstract

In this paper, we study the following nonlinear fractional Laplacian system with critical Sobolev-Hardy exponent (Formula presented.) where (Formula presented.) is a smooth bounded domain in (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) satisfy (Formula presented.), (Formula presented.) is the critical Sobolev-Hardy exponent, (Formula presented.), (Formula presented.) are parameters, (Formula presented.), (Formula presented.) and (Formula presented.) are nonnegative functions on (Formula presented.). Using the variational methods and analytic techniques, we prove that the critical fractional Laplacian system admits at least two positive solutions when the pair of parameters (Formula presented.) belongs to a suitable subset of (Formula presented.).

Original language	English
Pages (from-to)	3488-3512
Number of pages	25
Journal	Mathematical Methods in the Applied Sciences
Volume	43
Issue number	6
DOIs	https://doi.org/10.1002/mma.6134
State	Published - 01 04 2020

Bibliographical note

Publisher Copyright:
© 2020 John Wiley & Sons, Ltd.

Keywords

Nehari manifold
concave-convex nonlinearities
fractional Laplacian system
fractional critical Sobolev-Hardy exponent
multiple positive solutions

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10.1002/mma.6134

Cite this

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title = "Existence results for a fractional elliptic system with critical Sobolev-Hardy exponents and concave-convex nonlinearities",

abstract = "In this paper, we study the following nonlinear fractional Laplacian system with critical Sobolev-Hardy exponent (Formula presented.) where (Formula presented.) is a smooth bounded domain in (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) satisfy (Formula presented.), (Formula presented.) is the critical Sobolev-Hardy exponent, (Formula presented.), (Formula presented.) are parameters, (Formula presented.), (Formula presented.) and (Formula presented.) are nonnegative functions on (Formula presented.). Using the variational methods and analytic techniques, we prove that the critical fractional Laplacian system admits at least two positive solutions when the pair of parameters (Formula presented.) belongs to a suitable subset of (Formula presented.).",

keywords = "Nehari manifold, concave-convex nonlinearities, fractional Laplacian system, fractional critical Sobolev-Hardy exponent, multiple positive solutions",

author = "Jinguo Zhang and Hsu, \{Tsing San\}",

note = "Publisher Copyright: {\textcopyright} 2020 John Wiley \& Sons, Ltd.",

year = "2020",

month = apr,

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doi = "10.1002/mma.6134",

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T1 - Existence results for a fractional elliptic system with critical Sobolev-Hardy exponents and concave-convex nonlinearities

AU - Zhang, Jinguo

AU - Hsu, Tsing San

PY - 2020/4/1

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N2 - In this paper, we study the following nonlinear fractional Laplacian system with critical Sobolev-Hardy exponent (Formula presented.) where (Formula presented.) is a smooth bounded domain in (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) satisfy (Formula presented.), (Formula presented.) is the critical Sobolev-Hardy exponent, (Formula presented.), (Formula presented.) are parameters, (Formula presented.), (Formula presented.) and (Formula presented.) are nonnegative functions on (Formula presented.). Using the variational methods and analytic techniques, we prove that the critical fractional Laplacian system admits at least two positive solutions when the pair of parameters (Formula presented.) belongs to a suitable subset of (Formula presented.).

AB - In this paper, we study the following nonlinear fractional Laplacian system with critical Sobolev-Hardy exponent (Formula presented.) where (Formula presented.) is a smooth bounded domain in (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) satisfy (Formula presented.), (Formula presented.) is the critical Sobolev-Hardy exponent, (Formula presented.), (Formula presented.) are parameters, (Formula presented.), (Formula presented.) and (Formula presented.) are nonnegative functions on (Formula presented.). Using the variational methods and analytic techniques, we prove that the critical fractional Laplacian system admits at least two positive solutions when the pair of parameters (Formula presented.) belongs to a suitable subset of (Formula presented.).

KW - Nehari manifold

KW - concave-convex nonlinearities

KW - fractional Laplacian system

KW - fractional critical Sobolev-Hardy exponent

KW - multiple positive solutions

UR - https://www.scopus.com/pages/publications/85077884432

U2 - 10.1002/mma.6134

DO - 10.1002/mma.6134

M3 - 文章

AN - SCOPUS:85077884432

SN - 0170-4214

VL - 43

SP - 3488

EP - 3512

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 6

ER -

Existence results for a fractional elliptic system with critical Sobolev-Hardy exponents and concave-convex nonlinearities

Abstract

Bibliographical note

Keywords

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