A Note on Leighton's Variational Lemma for Fractional Laplace Equations

Abstract

In this note, we establish Leighton's variational lemma for fractional Laplace equations. We use the classical techniques to establish this variational lemma. We also point out several questions concerning the zeros of the solutions to fractional Laplace equations which play an important role in the qualitative theory of fractional Laplace equations.