Weak solutions for a nonlocal problem via the Galerkin method
In this article, we obtain some results of existence of solutions for the following fractional problem: {M(∫Rn×Rn|u(x)−u(y)|2|x−y|n+2s)(−Δ)su=fin Ω,u=0in Rn∖Ω, where n>2s with s∈(0,1), M:R→R is a function, Ω⊂Rn is a bounded open domain with smooth boundary, and f with suitable conditions. We study the existence of weak solutions, using the Galerkin method.
Authors
- Augusto César dos Reis Costa (ORCID: https://orcid.org/0000-0002-9798-5357)
- R. A. D. Guimarães (ORCID: https://orcid.org/0009-0005-2026-7225)
Institutions
- Universidade Federal do Pará (BR)
Publication Details
- Journal
- Complex Variables and Elliptic Equations
- Published
- 2026-08-20
- DOI
- https://doi.org/10.1080/17476933.2026.2717716
- Primary Topic
- Nonlinear Differential Equations Analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Conselho Nacional de Desenvolvimento Científico e Tecnológico