  We study qualitative properties of solutions to the fractional
Lane-Emden-Fowler equations with slightly subcritical exponents where the
associated fractional Laplacian is defined in terms of either the spectra of
Dirichlet Laplacian or the integral representation. As a consequence, we
classify the asymptotic behavior of all finite energy solutions. Our method
also provides a simple and unified approach to deal with the classical (local)
Lane-Emden-Fowler equation for any dimension greater than 2.
