Multiplicity results of fractional p-Laplace equations with\n sign-changing and singular nonlinearity

2016/04/04 by Sarika Goyal, Goyal, Sarika · 2 citations
Computer Science · Mathematics · #35A15 #35J75 #35R11 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Boundary value problem #Bounded function #Combinatorics #Differential Equations and Boundary Problems #Domain (mathematical analysis) #FOS: Mathematics #Fractional Laplacian #Mathematical analysis #Mathematical physics #Mathematics #Multiplicity (mathematics) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Physics #math.AP #msc:35A15 #msc:35J75 #msc:35R11 #p-Laplacian

paper · pdf · doi:10.48550/arxiv.1604.00801

published in arXiv (Cornell University) (Cornell University) · 24 pages

arxiv created 2016/04/04 · openalex publication_date 2016/04/04 · arxiv updated 2016/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this article, we study the following fractional p-Laplacian equation\nwith singular nonlinearity\n n (P
_la)
left
\- 2
int
_mb\nRⁿ
frac|w(y)-w(x)|^p-2(w(y)-w(x))|x-y|^n+psdy = a(x) w^-q+
la b(x)\nw^r
;
textin
;
Om
quad
quad w · gt;0
;
textin
;
Om,
quad w = 0
;\n
mboxin
;
mb Rⁿ
setminus
Om, \
quad
right. nwhere Om is a bounded domain in mb Rⁿ with smooth boundary \∂\n Om, n> ps,s\∈(0,1), la>0, 0<q<1, q<p-1<r< p_s^*-1 with\np_s^*=\(np)/(n-ps), a: Om\⊂ mb Rⁿ ra mb R such that 0<\na(x)\∈ L^ fracp^*_sp^*_s-1+q( Om), and b: Om\⊂ mb Rⁿ ra\n mb R is a sign-changing function such that b(x)\∈\nL^ fracp^*_sp^*_s-1-r( Om). Using variational methods, we show\nexistence and multiplicity of positive solutions of (P _la) with respect to\nthe parameter la.\n

Citations

• Existence, Uniqueness of Positive Solution to a Fractional Laplacians with Singular Nonlinearity
• Fractional p-eigenvalues
• Multiplicity of positive solutions for a fractional Laplacian equations involving critical nonlinearity
• Hitchhikerʼs guide to the fractional Sobolev spaces
• On a singular nonlinear elliptic boundary-value problem
• The Brezis-Nirenberg result for the fractional Laplacian

Cited by

• Multiplicity results for mixed local-nonlocal variable exponent problem involving singular and superlinear term
• Multiplicity results of fractional-Laplace system with sign-changing and singular nonlinearity

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