On fractional Laplacian problems with indefinite nonlinearity

Yongqiang Fu; Bingliang Li

doi:10.1080/00036811.2016.1249861

On fractional Laplacian problems with indefinite nonlinearity

Yongqiang Fu
, Bingliang Li^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

2 Scopus citations

Abstract

In this paper, we study the existence of positive solutions for the following Laplacian problem with indefinite nonlinearity (Formula presented.) where Ω ⊂ R^N is a bounded C^1,1 domain and a(x) is a sign-changing function. For suitable conditions on a(x) and p, we prove: there exists Λ > λ₁,s such that problem has a positive solution for λ_1,s ≤ λ < Λ and has no positive solution for λ > Λ, where λ_1,s is the first eigenvalue of the fractional Laplacian operator.

Original language	English
Pages (from-to)	2852-2868
Number of pages	17
Journal	Applicable Analysis
Volume	96
Issue number	16
DOIs	https://doi.org/10.1080/00036811.2016.1249861
State	Published - 10 Dec 2017

Keywords

Fractional Laplacian operator
indefinite nonlinearity
positive solution

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10.1080/00036811.2016.1249861

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title = "On fractional Laplacian problems with indefinite nonlinearity",

abstract = "In this paper, we study the existence of positive solutions for the following Laplacian problem with indefinite nonlinearity (Formula presented.) where Ω ⊂ RN is a bounded C1,1 domain and a(x) is a sign-changing function. For suitable conditions on a(x) and p, we prove: there exists Λ > λ1,s such that problem has a positive solution for λ1,s ≤ λ < Λ and has no positive solution for λ > Λ, where λ1,s is the first eigenvalue of the fractional Laplacian operator.",

keywords = "Fractional Laplacian operator, indefinite nonlinearity, positive solution",

author = "Yongqiang Fu and Bingliang Li",

note = "Publisher Copyright: {\textcopyright} 2016 Informa UK Limited, trading as Taylor \& Francis Group.",

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AU - Li, Bingliang

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Y1 - 2017/12/10

N2 - In this paper, we study the existence of positive solutions for the following Laplacian problem with indefinite nonlinearity (Formula presented.) where Ω ⊂ RN is a bounded C1,1 domain and a(x) is a sign-changing function. For suitable conditions on a(x) and p, we prove: there exists Λ > λ1,s such that problem has a positive solution for λ1,s ≤ λ < Λ and has no positive solution for λ > Λ, where λ1,s is the first eigenvalue of the fractional Laplacian operator.

AB - In this paper, we study the existence of positive solutions for the following Laplacian problem with indefinite nonlinearity (Formula presented.) where Ω ⊂ RN is a bounded C1,1 domain and a(x) is a sign-changing function. For suitable conditions on a(x) and p, we prove: there exists Λ > λ1,s such that problem has a positive solution for λ1,s ≤ λ < Λ and has no positive solution for λ > Λ, where λ1,s is the first eigenvalue of the fractional Laplacian operator.

KW - Fractional Laplacian operator

KW - indefinite nonlinearity

KW - positive solution

UR - https://www.scopus.com/pages/publications/84994093940

U2 - 10.1080/00036811.2016.1249861

DO - 10.1080/00036811.2016.1249861

M3 - 文章

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SN - 0003-6811

VL - 96

SP - 2852

EP - 2868

JO - Applicable Analysis

JF - Applicable Analysis

IS - 16

ER -

On fractional Laplacian problems with indefinite nonlinearity

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