  In this article we develop a concentration compactness type principle in a
variable exponent setup. As an application of this principle we discuss a
problem involving fractional `{\it $(p(x),p^+)$-Laplacian}' and power
nonlinearities with exponents $(p^+)^*$, $p_s^*(x)$ with the assumption that
the critical set $\{x\in\Omega:p_s^*(x)=(p^+)^*\}$ is nonempty.
