Boundary behavior of solutions to fractional <i>p</i>-Laplacian equation

Abstract In this work, a generalized Hopf’s lemma and a global boundary Harnack inequality are proved for solutions to fractional p -Laplacian equations. Then the isolation of the first <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mi>p</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(s,p)} -eigenvalue is shown in bounded open sets satisfying the Wiener criterion.