Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds

Let $(X,\omega )$ be a compact connected Hermitian manifold of dimension $n$. We consider the Bott-Chern cohomology and let $[\chi ] \in H^{1,1}{$\text{BC}$}(X; $\mathbb{R}$)$. We study the deformed Hermitian-Yang-Mills equation, which is the following nonlinear elliptic equation $\sum{i} \arctan (\lambda_i) = h(x)$,where$\lambda_i$aretheeigenvaluesof$\chi$ with respect to $\omega$.