Sign changing solutions of p-fractional equations with concave-convex nonlinearities

Abstract

We study the existence of sign changing solutions to the following p-fractional problem with concave-critical nonlinearities: (-/g=D/)U-s(p) = /g=m/|u|(q-1)u + |u|(P*)s(-2)u in /g=W/, u = 0 in R-N backslash /g=W/, where s /m=elem/ (0,1) and p /m=ge/ 2 are fixed parameters, 0 < q < p - 1,/g=m//m=elem/ R+ and p*(s) = Np/(N - ps)./g=W/ is an open, bounded domain in R-N with smooth boundary, N > ps.