Localized concentration of semiclassical solutions for double phase problems with nonlocal reaction
Abstract
Abstract This paper focuses on the study of multiplicity and localized concentration properties of positive solutions for the following singularly perturbed double phase problem with nonlocal Choquard reaction $$\begin{aligned} \left\{ \begin{array}{ll} -\epsilon ^{p}\Delta _{p} u-\epsilon ^{q}\Delta _{q} u +V(x)(|u|^{p-2}u+|u|^{q-2}u)\\ \quad =\epsilon ^{\mu -N}\left( \frac{1}{|x|^{\mu }}*G(u)\right) g(u),& \hbox {in}~\mathbb {R}^{N},\\ u\in W^{1,p}(\mathbb {R}^{N})\cap W^{1,q}(\mathbb {R}^{N}),u>0, & \hbox {in}~\mathbb {R}^{N},\\ \end{array} \right. \end{aligned}$$ - ϵ p Δ p u - ϵ q Δ q u + V ( x ) ( | u | p - 2 u + | u | q - 2 u ) = ϵ μ - N 1 | x | μ ∗ G ( u ) g ( u ) , in R N , u ∈ W 1 , p ( R
Fields of Study & Subjects
Differential Equations and Numerical Methods
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Analysis and Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 16
- Issue
- 2
- Publication date
- 18 March 2026
- Language
- EN