Classification of finite energy solutions to the fractional Lane–Emden–Fowler equations with slightly subcritical exponents

Abstract

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 the 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 \({>}2\).