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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.

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