Singular periodic solutions for the p-laplacian in a punctured domain

Shanming Ji; Yutian Li; Rui Huang; Jingxue Yin

doi:10.3934/cpaa.2017019

Singular periodic solutions for the p-laplacian in a punctured domain

Shanming Ji, Yutian Li, Rui Huang^*, Jingxue Yin

^*Corresponding author for this work

Department of Mathematics

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

1 Citation (Scopus)

Abstract

In this paper we are interested in studying singular periodic so-lutions for the p-Laplacian in a punctured domain. We find an interesting phenomenon that there exists a critical exponent pc = N and a singular ex-ponent qs = p - 1. Precisely speaking, only if p > pc can singular periodic solutions exist; while if 1 < p ≤ pc then all of the solutions have no singularity. By the singular exponent qs = p - 1, we mean that in the case when q = qs, completely different from the remaining case q 6= qs, the problem may or may not have solutions depending on the coefficients of the equation.

Original language	English
Pages (from-to)	373-392
Number of pages	20
Journal	Communications on Pure and Applied Analysis
Volume	16
Issue number	2
DOIs	https://doi.org/10.3934/cpaa.2017019
Publication status	Published - Mar 2017

Scopus Subject Areas

Analysis
Applied Mathematics

User-Defined Keywords

Critical exponent
Singular exponent
Singular periodic solutions

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10.3934/cpaa.2017019

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title = "Singular periodic solutions for the p-laplacian in a punctured domain",

abstract = "In this paper we are interested in studying singular periodic so-lutions for the p-Laplacian in a punctured domain. We find an interesting phenomenon that there exists a critical exponent pc = N and a singular ex-ponent qs = p - 1. Precisely speaking, only if p > pc can singular periodic solutions exist; while if 1 < p ≤ pc then all of the solutions have no singularity. By the singular exponent qs = p - 1, we mean that in the case when q = qs, completely different from the remaining case q 6= qs, the problem may or may not have solutions depending on the coefficients of the equation.",

keywords = "Critical exponent, Singular exponent, Singular periodic solutions",

author = "Shanming Ji and Yutian Li and Rui Huang and Jingxue Yin",

note = "The work of Y. Li is supported in part by a General Research Fund from Hong Kong Research Grants Council(No. 201513) and the HKBU Strategic Development Fund. The work of R. Huang and J. Yin are supported in part by NSF of China (No. 11071099) . The work of R. Huang is supported in part by NSF of China (No. 11671155), NSF of Guangdong (No. 2016A030313418), NSF of Guangzhou (No. 201607010207), CPSF (No. 2015M572301) and FRFCU (No. 2015ZM191). ",

year = "2017",

month = mar,

doi = "10.3934/cpaa.2017019",

language = "English",

volume = "16",

pages = "373--392",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

publisher = "American Institute of Mathematical Sciences",

number = "2",

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TY - JOUR

T1 - Singular periodic solutions for the p-laplacian in a punctured domain

AU - Ji, Shanming

AU - Li, Yutian

AU - Huang, Rui

AU - Yin, Jingxue

N1 - The work of Y. Li is supported in part by a General Research Fund from Hong Kong Research Grants Council(No. 201513) and the HKBU Strategic Development Fund. The work of R. Huang and J. Yin are supported in part by NSF of China (No. 11071099) . The work of R. Huang is supported in part by NSF of China (No. 11671155), NSF of Guangdong (No. 2016A030313418), NSF of Guangzhou (No. 201607010207), CPSF (No. 2015M572301) and FRFCU (No. 2015ZM191).

PY - 2017/3

Y1 - 2017/3

N2 - In this paper we are interested in studying singular periodic so-lutions for the p-Laplacian in a punctured domain. We find an interesting phenomenon that there exists a critical exponent pc = N and a singular ex-ponent qs = p - 1. Precisely speaking, only if p > pc can singular periodic solutions exist; while if 1 < p ≤ pc then all of the solutions have no singularity. By the singular exponent qs = p - 1, we mean that in the case when q = qs, completely different from the remaining case q 6= qs, the problem may or may not have solutions depending on the coefficients of the equation.

AB - In this paper we are interested in studying singular periodic so-lutions for the p-Laplacian in a punctured domain. We find an interesting phenomenon that there exists a critical exponent pc = N and a singular ex-ponent qs = p - 1. Precisely speaking, only if p > pc can singular periodic solutions exist; while if 1 < p ≤ pc then all of the solutions have no singularity. By the singular exponent qs = p - 1, we mean that in the case when q = qs, completely different from the remaining case q 6= qs, the problem may or may not have solutions depending on the coefficients of the equation.

KW - Critical exponent

KW - Singular exponent

KW - Singular periodic solutions

UR - http://www.scopus.com/inward/record.url?scp=85009446580&partnerID=8YFLogxK

U2 - 10.3934/cpaa.2017019

DO - 10.3934/cpaa.2017019

M3 - Journal article

AN - SCOPUS:85009446580

SN - 1534-0392

VL - 16

SP - 373

EP - 392

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 2

ER -

Singular periodic solutions for the p-laplacian in a punctured domain

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