# Greens function representation of nonlinear Poisson equation

Let $$L$$ be an operator and suppose the Green's function exists. That is there exist a function $$G$$ such that $$LG=\delta$$ where $$\delta$$ is the Dirac delta function. If $$L$$ is linear, one can represent the solution $$u$$ of the Poisson equation $$Lu=f$$ by $$u(x)=\int_{\Omega}G(x,y)f(y)dy$$ as discussed in the following link :https://en.wikipedia.org/wiki/Green%27s_function

My question is can we get the same representation of $$u$$ if $$L$$ becomes nonlinear?

Thank you very much in advance.