Calculus of Variations and Geometric Measure Theory
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Z. Liu - M. Squassina - J. Zhang

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

created by squassina on 23 Dec 2016
modified on 30 May 2017


Accepted Paper

Inserted: 23 dec 2016
Last Updated: 30 may 2017

Journal: NoDEA, Nonlinear Differential Equations Applications
Year: 2016


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.


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