On the Pohozaev identity for the fractional \(p\)-Laplacian operator in \(\mathbb{R}^N\). (English) Zbl 07922700
Summary: 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.
© 2024 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
© 2024 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
MSC:
| 35A15 | Variational methods applied to PDEs |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35R11 | Fractional partial differential equations |
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