In this paper, we show the existence of a nontrivial weak solution for a nonlinear problem involving the fractional $p$-Laplacian operator and a Berestycki–Lions type nonlinearity. This solution satisfies a Pohozaev identity. Moreover, we prove that any sufficiently smooth solution fulfills the Pohozaev identity.

中文翻译：

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RN 中分数 p-拉普拉斯算子的 Pohozaev 恒等式

在本文中，我们证明了涉及分数的非线性问题的非平凡弱解的存在性$p$-拉普拉斯算子和 Berestycki–Lions 型非线性。该解满足 Pohozaev 恒等式。此外，我们证明任何足够平滑的解决方案都满足 Pohozaev 恒等式。