Combined effects of the Hardy potential and lower order terms in fractional Laplacian equations

Boundary Value Problems

Canyun Huang¹  Shuibo Huang²  Yingyuan Mi² 

[1] Department of Applied Mathematics, Lanzhou University of Technology;School of Mathematics and Computer, Northwest Minzu University;

关键词: Fractional Laplacian;    Hardy potential;    Regularizing effect;   

DOI  :  10.1186/s13661-018-0980-4

来源: DOAJ

【 摘 要 】

Abstract In this paper we consider the existence and regularity of solutions to the following nonlocal Dirichlet problems: {(−Δ)su−λu|x|2s+up=f(x),x∈Ω,u>0,x∈Ω,u=0,x∈RN∖Ω, $$ \textstyle\begin{cases} (-\Delta)^{s} u-\lambda\frac{u}{|x|^{2s}}+u^{p}=f(x), &x\in\Omega, \\ u>0, &x\in\Omega, \\ u=0, & x\in\mathbb{R}^{N}\setminus\Omega, \end{cases} $$ where (−Δ)s $(-\Delta)^{s}$ is the fractional Laplacian operator, s∈(0,1) $s\in(0,1)$, Ω⊂RN $\Omega\subset\mathbb{R}^{N}$ is a bounded domain with Lipschitz boundary such that 0∈Ω $0\in\Omega$, f is a nonnegative function that belongs to a suitable Lebesgue space.

【 授权许可】

Unknown