Heat flow method for Lichnerowicz type equations on closed manifolds

In this paper, we establish existence results for positive solutions to the Lichnerowicz equations of the following type in closed manifolds

-Du = A(x)u-p - B(x)uq,    in M,-Delta u = A(x)u^{-p} - B(x)u^{q},quad {{rm in}}, M,
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