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I know Pohozaev-type identities are important tools for many PDEs including nonlinear, nonlocal problems, for showing nonexistence and uniqueness. However, is there any elementary reference on Pohozaev identity with applications? For example, I am interested in showing uniqueness of basic nonlinear PDE; model problem would be power type equation $$\begin{cases}(-\Delta) u=|u|^{p-1}u&\text{ in }\Omega\\ u=0&\text{ in }\Omega^c\end{cases}$$ via Pohozaev identity.

Thank you in advance.

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    $\begingroup$ Wikipedia article on Pokhozhaev identities has a reference list, including the original paper of Pokhozhaev which is available on Internet. $\endgroup$
    – Alexandre Eremenko
    Commented May 5, 2023 at 14:38

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