Abstract
In this paper, we concern with the existence of solutions of the complex $m$-Hessian type equation $-\chi(u) H_{m}(u) = \mu$ in the class $\mathcal{E}_{m,\chi}(f,\Omega)$ if there exists subsolution in this class, where the given boundary value $f \in \mathcal{N}_{m}(\Omega) \cap MSH_{m}(\Omega)$.
Funding Statement
The second named author is supported by the grant 101.02-2023.11 from the NAFOSTED (National Foundation for Science and Technology developments) program.
Acknowledgments
We wish to express our gratitude an anonymous referee for his/her careful reading and constructive comments that help to improve significantly our exposition.
Citation
Nguyen Van Phu. Nguyen Quang Dieu. "Complex $m$-Hessian Type Equations in Weighted Energy Classes of $m$-subharmonic Functions with Given Boundary Value." Taiwanese J. Math. Advance Publication 1 - 12, 2024. https://doi.org/10.11650/tjm/241204
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