On the Pohozaev identity for the fractional $p$-Laplacian operator in $\mathbb{R}^N$

Vincenzo Ambrosio

On the Pohozaev identity for the fractional $p$-Laplacian operator in $\mathbb{R}^N$

Analysis of PDEs 2024-04-05 v3

Authors: Vincenzo Ambrosio

Abstract

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.

Keywords

fractional p-laplacian pohozaev identity weak solution nonlinear problem berestycki-lions nonlinearity

Cite

@article{arxiv.2301.06537,
  title  = {On the Pohozaev identity for the fractional $p$-Laplacian operator in $\mathbb{R}^N$},
  author = {Vincenzo Ambrosio},
  journal= {arXiv preprint arXiv:2301.06537},
  year   = {2024}
}

Comments

to appear in Bulletin of the London Mathematical Society

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