Abstract
In this paper, we study the fractional p(x)-Laplacian problem with variable exponents
{(-Delta)(p(.))(s)u(x) + vertical bar u(x)vertical bar(q(x)-2)u(x) = lambda partial derivative F/partial derivative u(x,u), x is an element of Omega,
u(x) = 0, x is an element of partial derivative Omega.
Where Omega subset of R-N, N > 2 is a bounded smooth domain, F is an element of C-1 ((Omega) over bar x R, R) with lambda is a positive parameter and q is a continuous function on (Omega) over bar.