Quasilinear nonlocal elliptic problems with varable singular exponent

Prashanta Garain

doi:10.3934/cpaa.2020226

Quasilinear nonlocal elliptic problems with varable singular exponent

Prashanta Garain^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Qassim University

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

13 Citations (Scopus)

Abstract

In this article, we provide existence results to the following nonlocal equation (Formula presented) where (Formula presented) is the fractional p-Laplacian operator. Here Ω ⊂ R^N is a smooth bounded domain, s ∈ (0, 1), p > 1 and N > sp. We establish existence of at least one weak solution for (P_λ) when g(x, u) = f(x)u^−q^(x) and existence of at least two weak solutions when g(x, u) = λu−q(x⁾ + u^r for a suitable range of λ > 0. Here (Formula presented) where (Formula presented) is the critical Sobolev exponent and (Formula presented).

Original language	English
Pages (from-to)	5059-5075
Number of pages	17
Journal	Communications on Pure and Applied Analysis
Volume	19
Issue number	11
DOIs	https://doi.org/10.3934/cpaa.2020226
Publication status	Published - Nov 2020
MoE publication type	A1 Journal article-refereed

Keywords

Fractional p-Laplacian
Multiple weak solutions
Singular nonlinearity
Variable exponent
Variational method

Access to Document

10.3934/cpaa.2020226

Cite this

@article{bd348454ea994dcea9e5c16c5a4529e9,

title = "Quasilinear nonlocal elliptic problems with varable singular exponent",

abstract = "In this article, we provide existence results to the following nonlocal equation (Formula presented) where (Formula presented) is the fractional p-Laplacian operator. Here Ω ⊂ RN is a smooth bounded domain, s ∈ (0, 1), p > 1 and N > sp. We establish existence of at least one weak solution for (Pλ) when g(x, u) = f(x)u−q(x) and existence of at least two weak solutions when g(x, u) = λu−q(x) + ur for a suitable range of λ > 0. Here (Formula presented) where (Formula presented) is the critical Sobolev exponent and (Formula presented).",

keywords = "Fractional p-Laplacian, Multiple weak solutions, Singular nonlinearity, Variable exponent, Variational method",

author = "Prashanta Garain",

year = "2020",

month = nov,

doi = "10.3934/cpaa.2020226",

language = "English",

volume = "19",

pages = "5059--5075",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

publisher = "American Institute of Mathematical Sciences",

number = "11",

}

TY - JOUR

T1 - Quasilinear nonlocal elliptic problems with varable singular exponent

AU - Garain, Prashanta

PY - 2020/11

Y1 - 2020/11

N2 - In this article, we provide existence results to the following nonlocal equation (Formula presented) where (Formula presented) is the fractional p-Laplacian operator. Here Ω ⊂ RN is a smooth bounded domain, s ∈ (0, 1), p > 1 and N > sp. We establish existence of at least one weak solution for (Pλ) when g(x, u) = f(x)u−q(x) and existence of at least two weak solutions when g(x, u) = λu−q(x) + ur for a suitable range of λ > 0. Here (Formula presented) where (Formula presented) is the critical Sobolev exponent and (Formula presented).

AB - In this article, we provide existence results to the following nonlocal equation (Formula presented) where (Formula presented) is the fractional p-Laplacian operator. Here Ω ⊂ RN is a smooth bounded domain, s ∈ (0, 1), p > 1 and N > sp. We establish existence of at least one weak solution for (Pλ) when g(x, u) = f(x)u−q(x) and existence of at least two weak solutions when g(x, u) = λu−q(x) + ur for a suitable range of λ > 0. Here (Formula presented) where (Formula presented) is the critical Sobolev exponent and (Formula presented).

KW - Fractional p-Laplacian

KW - Multiple weak solutions

KW - Singular nonlinearity

KW - Variable exponent

KW - Variational method

UR - http://www.scopus.com/inward/record.url?scp=85092396988&partnerID=8YFLogxK

U2 - 10.3934/cpaa.2020226

DO - 10.3934/cpaa.2020226

M3 - Article

AN - SCOPUS:85092396988

SN - 1534-0392

VL - 19

SP - 5059

EP - 5075

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 11

ER -

Quasilinear nonlocal elliptic problems with varable singular exponent

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this