Finite Morse Index Solutions of the Fractional Henon–Lane–Emden Equation with Hardy Potential

Abstract

In this paper, we study the fractional Henon-Lane-Emden equation associated with Hardy potentialExtending the celebrated result of [14], we obtain a classification result on finite Morse index solutions to the fractional elliptic equation above with Hardy potential. In particular, a critical exponent p of Joseph-Lundgren type is derived in the supercritical case studying a Liouville type result for the s-harmonic extension problem.