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

2016/12/23 by Zhisu Liu, Marco Squassina, Liu, Zhisu +3
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1612.07914

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.

Citations

• The Brezis-Nirenberg result for the fractional Laplacian

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