SIGN-CHANGING SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM INVOLVING THE FRACTIONAL p-LAPLACIAN

In the paper, we consider the following boundary value problem involving the fractional p-Laplacian: (P) (-Delta)(p)(s)u(x) = f (x, u) in Omega, u(x) = 0 in R-N \ Omega. where Omega is a bounded smooth domain in R-N with N >= 1, (-Delta)(p)(s) is the fractional p-Laplacian with s is an element of (0, 1), p is an element of (1, N/s), f (x, u) : Omega x R -> R. Under the improved subcritical polynomial growth condition and other conditions, the existences of a least-energy sign-changing solution for the problem (P) has been established.