Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension

Zhisu Liu; Marco Squassina; Jianjun Zhang

Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension

Analysis of PDEs 2016-12-26 v1

Authors: Zhisu Liu , Marco Squassina , Jianjun Zhang

Abstract

We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential $V$ . Under suitable assumptions on $V$ , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti-Rabinowitz type condition or monotonicity assumptions.

Keywords

fractional Kirchhoff equation ground state critical nonlinearity external potential monotonicity trick profile decomposition Ambrosetti-Rabinowitz condition

Cite

@article{arxiv.1612.07914,
  title  = {Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension},
  author = {Zhisu Liu and Marco Squassina and Jianjun Zhang},
  journal= {arXiv preprint arXiv:1612.07914},
  year   = {2016}
}

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25 pages

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