Article Contents
Article Contents

# A Hopf type lemma and the symmetry of solutions for a class of Kirchhoff equations

This work was supported by NSFC grant 11771166, Hubei Key Laboratory of Mathematical Sciences, Program for Changjiang Scholars and Innovative Research Team in University #IRT_17R46 and China Scholarship Council
• In this paper, we proved a fractional Kirchhoff version of Hopf lemma for anti-symmetry functions and applied it to prove the symmetry and monotonicity of solutions for fractional Kirchhoff equations in the whole space by method of moving planes. We also obtain radially symmetry and monotonicity of solutions for fractional Kirchhoff equations in the unit ball. As far as we know, this is the first time to apply direct method of moving planes to fractional Kirchhoff problems.

Mathematics Subject Classification: Primary: 35J60, 35B06.

 Citation:

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