Solving Yamabe Problem by An Iterative Method

We introduce an iterative scheme to prove the Yamabe problem $ - a\Delta_{g} u + S u = \lambda u^{p-1} $,firstlyonopendomain$ (\Omega, g) $ with Dirichlet boundary conditions, and then on closed manifolds $(M,g)$ by local argument. It is a new proof, which solves the Yamabe problem for $ n \geqslant 3 $ in a uniform argument, beyonds the traditional analysis with respect to the minimization of functionals.