Work

Lower order term for the fractional Laplacian with a Hardy potential

Year: 2026

Type: article

Abstract: This paper is concerned with the following semilinear elliptic equation involving the fractional Laplacian: $$(-Δ)^s u+ g|u|^{p-1}u= λ\frac{u}{|x|^{2s}}+f(x),$$ in a bounded domain $Ω$ of $\mathbb{R}^N\,(N>2s)$, subject to the zero Dirichlet condition in $\mathbb{R}^N\setminus Ω$, where $01$ and $f\in L^{(p+1)/p}_g(Ω)$. Under certain integrability condition on $g$, the existence of solution is proven for every $λ\in \mathbb{R}$. Moreover, the regularity of solution is also obtained.

Source: Nonlinear Analysis

DOI: 10.1016/j.na.2026.114267

Authors: Rubén Fiñana, Alexis Molino

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,690

Funders: Junta de Andalucía, Universidad de Almería

Award: G9000379313