Abstract
This paper deals with the existence of multiple solutions for the following critical fractional p-Laplacian problem
{ (-Delta)(p)(s)u(x) = lambda vertical bar u vertical bar(p-2) u + f (x, u) + mu g(x, u) in Omega, u > 0,
u = 0 on R-n \ Omega,
where p > 1, s is an element of (0, 1), Omega subset of R-n (n > ps), be a bounded smooth domain, lambda, mu are positive parameters and the functions f, g : (Omega) over bar x [0, infinity) -> [0, infinity), are continuous and differentiable with respect to the second variable. Our main tools are based on variational methods combined with a classical concentration compacteness method.