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The main purpose of this work is to study a non-local scalar field equation in bounded domains. More precisely we consider the semi-linear fractional elliptic problem: (−Δ)su=λup−1−um−1 in Ω,u>0 in Ω, and u=0 in RN∖Ω, where Ω is a regular bounded domain of RN, m>p>2 and λ>0. We discuss the existence, non-existence, and multiplicity of solutions, for the largest possible range of the parameters λ,p,m.
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Batahri et al. (2024) studied this question.
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