A Choquard equation with an almost periodic term
Year: 2026
Type: article
Abstract: We consider the existence of nontrivial solution u ∈ H 1 ( R N ) $u\in {H}^{1}\left({\mathbb{R}}^{N}\right)$ for the following nonlinear Choquard equation with an almost periodic term − Δ u + u = I μ ∗ ( α ( y ) F ( u ) ) α ( x ) f ( u ) in R N , $$-{\Delta}u+u=\left({I}_{\mu }\ast \left(\alpha \left(y\right)F\left(u\right)\right)\right)\alpha \left(x\right)f\left(u\right)\quad \text{in}\quad {\mathbb{R}}^{N},$$ where N ≥ 3, μ ∈ (0, N ), I μ is the Riesz potential, F is the primitive function of f , and α is almost periodic. As one will see, almost periodic functions of several variables lack some important features of periodic functions and almost periodic functions on R $\mathbb{R}$ . This makes our problem more intriguing and challenging.
Source: Advanced Nonlinear Studies
Institutions: Gannan Normal University, Jiangxi Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,469
Awards: G1028838811, G42477289
OpenAlex ID: W7161573896