Theoretical analysis demonstrates the existence of weak solutions for nonlocal fractional problems in bounded domains, highlighting the utility of the Galerkin approximation 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.
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Costa et al. (2026) studied this question.
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