Existence of Two Positive Solutions for Two Kinds of Fractional p -Laplacian Equations

The aim of this paper is to investigate the existence of two positive solutions to subcritical and critical fractional integro-differential equations driven by a nonlocal operator LKp. Specifically, we get multiple solutions to the following fractional p-Laplacian equations with the help of fibering maps and Nehari manifold. -Δpsux=λuq+ur,u>0 in Ω,u=0,in ℝN\Ω. Our results extend the previous results in some respects.