The research demonstrates existence of solutions to the weighted m-Hessian equation in m-subharmonic functions, implying broader applicability of the subsolution theorem.
In this paper, we concern with the existence of solutions of the weighted complex m-Hessian equation -χ(u)Hₘ(u)=μ in the class Em,χ(f,Ω) if there exists subsolution in this class, where the given boundary value fₘ(Ω)∩ MSHₘ(). This is a generalization of the result in the paper {PDtaiwan} where we proved that the subsolution theorem is true in the class Em,χ(f,Ω) in the case when the given boundary value fₘ(Ω)∩ MSHₘ().
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Nguyen Van Phu (2025) studied this question.
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