Abstract
This paper deals with the existence and multiplicity of nontrivial solutions to the following 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 on R-n\Omega,
where Omega subset of R-n(n > ps), is a bounded smooth domain, s is an element of (0, 1), lambda, mu are positive parameters, and f, g : (Omega) over bar x [0, infinity) -> R, are continuous functions. Using variational methods, especially, fibering maps and Nehari manifold, we obtain existence results for either, subcritical and critical cases. The results of the present paper, extend previous works which have recently appeared in the literature.