Unbalanced (p,2)-fractional problems with critical growth

2020/01/21 by Deepak Kumar, Kumar, Deepak, K. Sreenadh +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2001.07314

openalex publication_date 2020/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the existence, multiplicity and regularity results of non-negative solutions of following doubly nonlocal problem: (P_\la) \ \ds (-Δ)s1u+\ba (-Δ)s2pu = \la a(x)|u|q-2u+ (∫\Om(|u(y)|r)/(|x-y|μ)~dy)|u|r-2 u in \Om, u =0 in \mb Rn∖ \Om, . where \Om⊂\mb Rn is a bounded domain with C2 boundary \pa\Om, 0 2 s1, 1< q0 and a∈ L(d)/(d-q)(\Om), for some q

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• The Brezis-Nirenberg result for the fractional Laplacian

Related

• Unbalanced fractional elliptic problems with exponential nonlinearity: subcritical and critical cases
• Regularity and multiplicity results for fractional (p,q)-Laplacian equations
• Three solutions for a nonlocal problem with critical growth
• Existence of at least k solutions to a fractional p-Kirchhoff problem involving singularity and critical exponent
• Critical (p,q)-fractional problems involving a sandwich type nonlinearity