Quasilinear nonlocal elliptic problems with varable singular exponent

Prashanta Garain; Tuhina Mukherjee

doi:10.3934/cpaa.2020221

Quasilinear nonlocal elliptic problems with varable singular exponent

Prashanta Garain
, Tuhina Mukherjee

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

17 Scopus citations

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.2020221
State	Published - 1 Nov 2020
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2020221

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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 and Tuhina Mukherjee",

year = "2020",

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doi = "10.3934/cpaa.2020221",

language = "English",

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journal = "Communications on Pure and Applied Analysis",

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T1 - Quasilinear nonlocal elliptic problems with varable singular exponent

AU - Garain, Prashanta

AU - Mukherjee, Tuhina

PY - 2020/11/1

Y1 - 2020/11/1

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

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DO - 10.3934/cpaa.2020221

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

ASJC Scopus subject areas

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