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

TL;DR

This paper proves the existence of ground states for a nonlinear fractional Kirchhoff equation with critical nonlinearity in low dimensions, using advanced variational methods without relying on common growth conditions.

Contribution

It introduces new existence results for ground states in fractional Kirchhoff equations without the Ambrosetti-Rabinowitz condition.

Findings

Existence of ground states established under broad conditions

Use of monotonicity trick and profile decomposition techniques

Applicable to equations with critical nonlinearity in low dimensions

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.